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effective cost of borrowing

You borrowed a home loan of $1638949 from Monash Bank for 25 years at a 10% nominal annual interest rate, compounded monthly. Monash bank charged 3.5% points on any home loans on the day of issuing. If you receive an extra-large income increase after 15 years of payments and want to pay off the rest of this debt at once immediately. What is the annual effective cost of this borrowing?
contract loan amount	1,638,949.00	Step 1	Original PMT	Step 3	Finally payment if prepay
contract interest	10%	PV	1,638,949.00	N	120.00
point charge	3.50%	I	0.0083333333	I	0.0083333
Original terms	25.00	N	300.00	PMT	($14,893.14)
prepay in	15.00	PMT	($14,893.14)	PV	$1,126,981.36
		Step 2	Bank actually Lend	Step 4	compute the effective rate
		Contract amount	1,638,949.00	PV	1,581,585.79
		point	3.50%	N	180.00
		PV	1,581,585.79	PMT	($14,893.14)
				FV	($1,126,981.36)
				I	0.88%
				yearly	10.51%

Point Charge

A loan amount of $240,000 with an ordinary term of 30 years at rate of 8%. 但是8%只是写在贷款合同之中为了吸引borrower，如果lender自己想要达到的预期收益率为8.5%，how many points are needed？
		Step 1	Original PMT
contract loan amount	240,000.00	PV	240,000.00
contract interest	8%	I	0.0066666667
Original terms	30.00	N	360.00
		PMT	($1,761.03)
lender actually want	8.50%
		Step 2	Bank actually Lend
		N	360.00
		I	0.0070833
		PMT	($1,761.03)
		PV	$229,029.01
		Step 4	Compute the charge point
		PV	$229,029.01
		contract amount	240,000.00
		point charge	4.57%

RORAC

A business borrower would like to apply for a 10-year $10 million loan to finance its new project form BB Bank. BB bank would like to charge this borrower a 1% spread and 0.5% of origination fee and expect a 0.2% of the expected loss. Since the project is very complicated to evaluate, and it will cost BB bank $18,000 to invite experts to assess it. Suppose that the risk-adjuested factor (ΔR)/(1+RL) and the tax rates are 1% and 28% respectively, what is the RORAC of this borrower?
		%	Amount
	Spread	1.00%	100,000.00
	Fees	0.50%	50,000.00
	expected loss	0.20%	20,000.00
	operating cost	0.18%	18,000.00
	tax rate	28%
	分子部分	80,640.00
	duration	10
	loan value	10,000,000
	risk-adjusted factor	1%
	分母	1,000,000.00
	RORAC	8.06%

Prob of Repayment

A Company would like to borrow a $1 million loan from the bank for 3 years. This borrowe has a BBB credit rating on the bond market. The bank has collected related corporate bond returns and government bond returns, presented in the following table.
Table 1 Bond ratings and return rates with different maturities
	1 year	2 Year	3 Year	4 Year	5 Year
AAA	3.50%	4.20%	4.30%	5.45%	6.60%
AA	3.60%	4.60%	4.80%	5.55%	6.90%
A	4.10%	4.90%	5.50%	5.95%	7.20%
BBB	5.30%	5.60%	5.80%	6.50%	7.90%
BB	6.00%	6.50%	6.80%	7.55%	8.10%
B	7.00%	7.50%	8.80%	9.55%	10.10%
CCC	7.50%	7.90%	8.90%	10.55%	11.10%
CC	7.80%	8.80%	9.60%	10.50%	12.80%
Governement Bond	1.50%	2.70%	3.10%	3.90%	4.20%
If the loan is granted, what's the probability of default of this loan at maturity date?
Select one
a	3.61%
b	96.39%
c	5.42%
d	7.46%
e	none of above
	做题过程
	Year	Government Bond				分子	分母		prob. of repayment
	1	0.015			i0,1			0.015	0,1	0.9639126306
	2	0.027			i1,2	1.054729	1.015	0.0391418719	1,2	0.9812403071
	3	0.031			i2,3	1.095912791	1.054729	0.0390467988	2,3	0.9783763407
									Cumulative Prob. of Repayment	0.9253776216
	Year	BBB							prob of default	0.0746223784
	1	0.053			r0,1			0.053
	2	0.056			r1,2	1.115136	1.053	0.059008547
	3	0.058			r2,3	1.184287112	1.115136	0.0620113708

KMV

XXX Ltd. has banked with Bank of Australia for more than 10 years. XXX Ltd. would like to apply for a $ 10 million loan from the Bank of Australia and provides the following balance sheet report to the bank (in Table 1). It’s estimated that XXX Ltd. will have a growth rate of 15% in the coming year. The bank is provided the Expected Default Frequency Table from Moody (in Table 2).
Table 1		Table 2
Balance Sheets		Expected Default Frequency From Moody's
As at the end of Year	2019
	$ m	Distance to Default	Expected Default Frequency
Current Assets		1	50%
Cash	50	2	35%
Debtors	150	3	10%
Stock	240	4	5%
Current liabilities		5	2%
Creditors	220	6	1%
Hire Purchase	50	7	0.10%
Bank Overdraft	120	8	0.05%
Directors' Loans	14	9	0.01%
Current Tax	1
Net Current Assets	35	Suppose that the current market value of assets is $1100 million and its standard deviation is 12%. What’s the Expected Default Frequency of this borrower under the KMV model?
Fixed Assets
Freehold Building	120	Answer: 2% - 过程如下
Plant & Machinery	150	Current liabilities	405
		Long Term Liabilities	115
Long Term Liabilities
Mortgage Loan	50	Default point	462.5
Deferred Taxation	5
Corporate Bonds	60
Net Long Assets	155	Current Market Value of Asset	1100
		Growth Rate	15%
Net Assets	190
Financed by		Expected Market value of Asset	1265 Sushi: Sushi: 有的题目直接会给出来Future Market value of Asset / Expected Market value of Asseet 这种情况之下，题目仍给出Growth Rate就是迷惑的选项
Issued Share Capital	100
Profit and Loss Account	90
Total Capital	190	Volatility of Asset(%)	12% Sushi: Sushi: 有的题volatility直接给数字，那就直接用具体的数字做DD的分母
		Distance to Default	5.2865612648
Profit & Loss Amount Summary		分子部分	802.5
	$ m	分母部分	151.8
Sales	1300
COGS	1050
including Credit Purchase	800	DD为5.28，四舍五入为5，对应Table 2，找到EDF为2%
Gross Profit	150
EBIT	74
Interest	10
Net Profit before Tax	60

Builder-minimum finance require

King Builder specialized in office building construction for more than 10 years, has been banking with Banks of Australia for over 5 years. It has been recently been awarded a contract to build an office building for JP Morgan. The total contract price is $130 million and the construction length will be 13 months. It is expected that labor costs and material costs will be 60 percent and 40 percent of costs, respectively. It is estimated that the King Builder will make a profit of twenty-five (25) percent of the contract value. As this is a relatively straightforward project for this builder, it is safe to assume that construction progress will be spread evenly over the life of the project. Assume that monthly certificates will be issued at the end of the month and payments will occur 25 days after the issue of each certificate. A retention fund has been set up which will require retentions at the rate of 5 percent of the monthly payments and a minimum level 7 percent of the total contract value at the beginning of the construction. As a well-established builder, King Builder expects no difficulties in obtaining two-month credit terms from the suppliers of the necessary construction materials. What’s the minimum finance required of this builder at the end of the first month?
Total Contract Price	150,000,000		每个同学这一题的条件，最后的问题都会不一样，需要根据自己的题目调整计算思路
Duration	13			1月发生	2月发生	3月发生
Initial retention	7%	10,500,000	OUTFLOW
			Initial Retention	10,500,000
Profit	25%	37,500,000	累计的人工费	5,192,308	5,192,308	5,192,308
Cost of construction	75%	112,500,000	累计的材料费	0 Sushi: Sushi: 材料费有两个月的赊销期限	0	3,461,538
Labor	60%	67,500,000	TOTAL OUTFLOW	15,692,308	5,192,308	8,653,846
Materials	40%	45,000,000	Cumulative TOTAL OUTFLOW	15,692,308	20,884,615	29,538,462
			INFLOW
Monthly Payment	11,538,462		Net Monthly Payment	0	0	10,961,538
Monthly Retention	5%	576,923
Net Monthly payment	10,961,538		Finance require	15,692,308	20,884,615	18,576,923
Monthly labor cost	5,192,308
Monthly material cost	3,461,538	2 month credit term

minimum finance required at the end of the first month

Builder - Maximum loan amount

XXX is a builder and will complete one construction for its customer. It has 13 months to complete the building. The total contract price is $216 million. It is estimated that XXX will make a profit of 25% of the contract value. Labour costs and material costs are expected to be 65% and 35% of the construction costs, respectively. As this is a relatively striaghtforward project for XXX, it is safe to assume that construction progress will be spread evenly over the life of the project.
Interim payment certificates will be issued at the end of each month, and the corresponding payments received from its customer will occur two months after the issue of the progress certificate. Eve Meng: Sushi: 每月底验工发证，发证再两个月收到相对应的工程款也就是第一次收到工程款应该是在第三个月底/第四个月初稳妥一些，应该算作是第四个月的inflow
At the beginning of the project, the retention fund of XXX should have 10% of the total contract value. Additionally, XXX has to set up a retention fund which will require retentions at the rate of 8% of the monthly paymanets. As a well-established construction company, XXX expects no difficults in obtaining two-month credit terms form the suppliers of the necessary construction materials.
The bank's policy requires that XXX should provide at least 60% of the total cash requirements (as its own equity) for projects like this. What's the maximum loan amount that the bank will grant to XXX?
Total Contract Price	216,000,000		每个同学这一题的条件，最后的问题都会不一样，需要根据自己的题目调整计算思路
Duration	13			1月发生	2月发生	3月发生	4月发生
Initial retention	10%	21,600,000	OUTFLOW
			Initial Retention	21,600,000
Profit	20%	43,200,000	累计的人工费	8,640,000	8,640,000	8,640,000	8,640,000
Cost of construction	80%	172,800,000	累计的材料费	0 Sushi: Sushi: 材料费有两个月的赊销期限	0	4,652,308	4,652,308
Labor	65%	112,320,000	TOTAL OUTFLOW	30,240,000	8,640,000	13,292,308	13,292,308
Materials	35%	60,480,000	Cumulative TOTAL OUTFLOW	30,240,000	38,880,000	52,172,308	65,464,615
			INFLOW
Monthly Payment	16,615,385		Net Monthly Payment	0	0	- 0	15,286,154
Monthly Retention	8%	1,329,231
Net Monthly payment	15,286,154		Finance require	30,240,000	38,880,000	52,172,308 Eve Meng: Sushi: 在这几个月中，累积到第三个月，需要的资金是最多这个金额是builder的 minimum finance require	Eve Meng: Sushi: 每月底验工发证，发证再两个月收到相对应的工程款也就是第一次收到工程款应该是在第三个月底/第四个月初稳妥一些，应该算作是第四个月的inflow	Sushi: Sushi: 材料费有两个月的赊销期限	50,178,462
Monthly labor cost	8,640,000			Builder contribution		60%
Monthly material cost	4,652,308	2 month credit term		Bank can provide		40%
				Maximum loan amount		20,868,923

Return rate of loan

The Contractually Promised return on a loan
BB bank has granted a $1 m loan to APPLE CO. with an annual 0.09 loan rate. The bank keeps a capital ratio of 8%, and requires a minimum compensating balance ratio of 0.1. APPLE CO. has paid $5600 as loan origination fee to the bank. What is the gross return rate of this loan?
解题过程
其实就是求k
	以下首先全部换算为百分数	amount	principal	%
分子	loan Origination fee (f)	5,600.00	1,000,000.00	0.0056
	Base Rate (BR) Sushi: Sushi: BR + m 其实就是 loan contract 上面给到 borrower 的利率在这题目中 0.09 的 loan rate，就已经是 BR + m 的总和了			0.09 Eve Meng: Sushi: BR + m 总和为 loan contract 上面给到 borrower 的利率在这题目中 0.09 的 loan rate，就已经是 BR + m 的总和了
	Sushi: Sushi: BR + m 其实就是 loan contract 上面给到 borrower 的利率在这题目中 0.09 的 loan rate，就已经是 BR + m 的总和了	Credit risk premium (m)
				0.0956
分母	Compensating balance requirements (b)			0.1
	Reserve requirement (R)			0.08
				0.908
	Gross return (k)			0.1052863436

MMR Bond Price

Banana Ltd. Is rated as BBB on the bond market and the face value of the bond is $100 with a 6% coupon rate. Given that the risk-free rate is 4% annually and the bond will mature in 3 years. The mortality rates are provided in the following table
Cumulative Mortality Rates by Corporate Bond Ratings
	Years after Issuance
	1	2	3	4	5	6
AAA	0.00%	0.00%	0.00%	0.00%	0.03%	0.03%
AA	0.00%	0.00%	0.32%	0.48%	0.51%	0.54%
A	0.01%	0.11%	0.42%	0.51%	0.65%	0.74%
BBB	0.36%	3.11%	4.12%	5.51%	6.65%	7.34%
BB	1.21%	3.48%	4.42%	6.41%	8.65%	10.24%
What's the current price of Banana Ltd's bonds?
Year	cash flow	mortality rate	surval cash flow	PV
1	6	0.0036	5.9784	5.7484615385
2	6	0.0311	5.8134	5.3748150888
3	106	0.0412	101.6328	90.3511891215
			Price	101.4744657487

Cumulative Mortality Rate

ABC Ltd. is rated as AAA on the bond market, and the face value of the bond is $100 with a 7% coupon rate. Given that the risk-free rate is 3.5% annually and the bond will mature in 5 years. The marginal mortality rates are provided in the following table
	Table: Marginal Mortality Rates by Corporate Bond Ratings
		Years after issuance
		1	2	3	4	5	6
	AAA Marginal Rates	0.00%	0.01%	0.05%	0.06%	0.09%	0.10%
	AA Marginal Rates	0.04%	0.08%	0.32%	0.48%	0.51%	0.54%
	A Marginal Rates	0.09%	0.22%	0.72%	0.81%	1.95%	2.74%
	BBB Marginal Rates	0.36%	3.11%	4.12%	5.51%	6.65%	7.34%
	BB Marginal Rates	1.21%	3.48%	4.42%	6.41%	8.65%	10.24%
	B Marginal Rates	2.52%	5.44%	7.12%	8.82%	7.32%	6.19%
	CCC Marginal Rates	7.55%	14.81%	18.28%	13.76%	9.54%	7.33%
What is the cumulative mortality rate of ABC Ltd's bond?
		1	2	3	4	5
	AAA Marginal Rate	0.00%	0.01%	0.05%	0.06%	0.09%
		100.00%	99.99%	99.95%	99.94%	99.91%
	cumulative survival rate
	99.7901489601027%
	cumulative mortality rate
	0.209851039897291%

Rating Migration

	The Corporate Bonds of Banana company are rated as A rating on the market, and a table of transitions probabilities to different ratings and market values in provided below.
	Ratings	Transition Probability	Market Value $
	AAA	0.19% Sushi: Sushi: Banana公司的债券，评级变为AAA的可能性为0.19% 下同	108.00 Sushi: Sushi: 当前AAA类别的债券市价为108 若Banana的债券被评为AAA的情况下，市价为108 下同
	AA	0.43%	107.00
	A	91.00% Sushi: Sushi: 现在Banana的债券评级为A，因此评级保持为A的可能性是最高的	106.00
	BBB	3.00%	105.00
	BB	4.00%	100.00
	B	1.20%	90.00
	C	0.12%	80.00
	Default	0.06%	50.00
	What is should be the price of this Banana Corporate bonds if considering the possible rating migration?
以上表格的解读为：市场价格变为108的概率为0.19%，等等。因此考虑了评级变化之后的价格就是以上表格的加权平均
	Ratings	Transition Probability	Market Value $	weighted value
	AAA	0.19%	108.00	0.2052
	AA	0.43%	107.00	0.4601
	A	91.00%	106.00	96.46
	BBB	3.00%	105.00	3.15
	BB	4.00%	100.00	4
	B	1.20%	90.00	1.08
	C	0.12%	80.00	0.096
	Default	0.06%	50.00	0.03
			Price	105.4813

Z socre

Consider the following data of a prospective borrower. Applying Altman's Z score. What is this company's Z score (round to two decimal)?
Curren Assets	490,300
Fixed Assets	4,006,000	Selected one
Total Assets	4,496,300	a	3.41
Current Liabilities	187,300	b	3.18
Long-term Liabilities	3,000,100	c	3.86
Liabilities	3,187,400	d	2.15
Book value of Equity	1,308,900	e	2.61		每个变量	系数
Working Captial	400,000			X1	0.0889620355	1.2	0.1067544425
sales	8,000,000			X2	0.0144563308	1.4	0.0202388631
EBIT	500,000			X3	0.1112025443	3.3	0.3669683962
Retained Earnings	65,000			X4	0.56	0.6	0.3388341595
Number of Shares	100,000			X5	1.779240709	1	1.779240709
Price per share	18					Z-score	2.6120365704

Regression model

Given the following regression model:
Pi = 0.8Current Ratio + 0.4Gross Margin + 0.3*(Equity/Debt)
Where Pi is the probability of repayment. The balance data of ABC Ltd. is shown in the following table
	$
Curren Asset	150,000
Non current Assets	450,000
Total Asset	600,000
Equity	240,000
Current Liabilities	250,000
Book value of liabilities	360,000
Sales revenue	1,000,000
Gross income	15,000
EBIT	250,000
What is the probability of default of this company?
系数	变量值
0.8	0.6	0.48
0.4	0.015	0.006
0.3	0.6666666667	0.2
Prob. of repayment		0.686
Prob. of default		0.314

Topic 9 - Restruor liqu

Case 1			Case 2
Company A Ltd. owes Monash bank $300 and is in financial distress now. The owner of Company A has some special skills to run the firm, that costs him $15. With these skills, firm value can be $315 with a probability of 0.8, otherwise 0. The liquidation value of the firm is $200			Monash bank again is having problem with Company A Ltd.. Now Company A Ltd. Owes senior bond holders $75 and Monash bank $500. It still costs Company A Ltd. $15 to run the company, if it continues, the firm will be worth $520 with a probability 0.75, otherwise 0. The liquidation of the firm is $90 and the firm wants to default.
priority: Bank > shareholder			priority: senior > junior > shareholder
Monash Bank	300		Senior bondholder	75
			Monash Bank(junior)	500
If liquidate the firm	200
If Continue:			If liquidate	90
Cost	-15		If Continue:
Success	315	0.8	Cost	-15
Failure	0	0.2	Success	520	0.75
Fisrt Step			Failure	0	0.25
Choices of shareholders:
Continue	-3		Fisrt Step
Liquidation	0		Choices of shareholders:
			Continue	-15
Choices of monash Bank			Liquidation	0
Continue	240
Liquidation	200		Choices of senior bondholder
			Continue	56.25
Second Step: Negociation and restructure			Liquidation	75
Restructure the debt with the shareholders, make him continue the business			Choices of junior debtholder(monash)
			Continue	333.75
Break Even point if Owner choose to continue			Liquidation	15		Loss	-485
-15 + (315 - New Loan)0.8 + 00.2 = 0
Monash will reduce its New Loan to	296.25
			Second Step: Negociation and restructure
expected value of monash if restructure the loan	237
			1. Overtake the bond
			New debt owed by Monash	575
			2. Convince the Shareholder
			Break Even point if Owner choose to continue
			-15 + (520 - New Loan)0.75 + 00.25 >= 0
			Monash (junior) will reduce its New Loan to	<= 500
			expected value of monash if restructure the loan	375		Loss	200

Topic 10 Basket Swap

Assume the following reference credit portfolio:
Credit 1: $100,000 notional, post-default value $31120.8
Credit 2: $200,000 notional, post-default value $51179.6
Credit 3: $250,000 notional, post-default value $89458.7
Given a $550,000 structure, if credits 2 ans 3 default in a second-to-default basket (in that order), how much will an investor receive?
此题说到的现在是一个second-to-default basket，所以只会对第二个违约的进行赔偿，因此只赔偿Credit 3违约的部分
Credit 3	notional	post-default value Eve Meng: Sushi: 违约之后的价值	赔偿金额
	250,000.00	89,458.70	160,541.30

Topic 10 credit spread option

Senario 1

If an investor buys a 12-month credit spread call option on Company ABC’s bond with a strike spread of 100bps for a premium of 35 bps, what is the appropriate course of action if ABC’s spread tightens to 50bps? Widens to 150bps? What is the breakeven level of the trade?

Spread tighten: the investor should exercise the right

Then the investor can get the net gain of 15bps (100bps – 50bps – 35bps)

Spread widen: the investor should abandon the right

Breakeven level:

100𝑏𝑝𝑠 – 35𝑏𝑝𝑠 = 65 𝑏𝑝𝑠

Each 1bp tighten after 65 bps generates profit

Senario 2

If an investor buys a 12-month credit spread put option on Company ABC’s bond with a strike spread of 100bps for a premium of 35 bps, what is the appropriate course of action if ABC’s spread tightens to 50bps? Widens to 150bps? What is the breakeven level of the trade?

Spread tighten: the investor should abandon the right

Spread widen: the investor should exercise the right

Then the investor can get the net gain of 15bps (150bps – 100bps – 35bps)

Breakeven level:

100𝑏𝑝𝑠 – 35𝑏𝑝𝑠 = 65 𝑏𝑝𝑠

Each 1bp widen from 65 bps generates profit