Need some to review assignment

The first section of the test asks you to address these discounted cash flow analysis problems:

1. What is the present value of the following uneven cash flow stream −$50, $100, $75, and $50 at the end of Years 0 through 3? The appropriate interest rate is 10%, compounded annually.

Formula to calculate PV of single cash flow is PV=fv/ (1+i) n

PV = $50 + 100/ (1+.1)1+ 75/ (1+.1)2 + 50/ (1+.1)3

50+ 90.909 + 61.98 + 37.56

$240.45

2. We sometimes need to find out how long it will take a sum of money (or something else, such as earnings, population, or prices) to grow to some specified amount. For example, if a company’s sales are growing at a rate of 20% per year, how long will it take sales to double?

The formula of 72 Rule is as follows:

72 = n*i

72 = n * 20

N = 72/20

N= 3.6 years.

3. Will the future value be larger or smaller if we compound an initial amount more often than annually—for example, every 6 months, or semiannually—holding the stated interest rate constant? Why?

The future value of an amount will go on increasing as the compounding frequency gets greater than one. If interest is being compounded semiannually, quarterly, weekly or monthly the reason for higher future value is that the compound interest means interest on interest as the compounding frequency continues increasing. If the interests is compounded semiannually then interest amount will be higher than if interest is compounded annually so interest on that higher amount will be higher and so on. Thus future value of amount having interest compounded quarterly will be higher than if the same amount is being compounded semiannually and so on.

4. What is the effective annual rate (EAR or EFF%) for a nominal rate of 12%, compounded semiannually? Compounded quarterly? Compounded monthly? Compounded daily?

Effective interest rate = (1 + i/m) m – 1

Semiannually = (1 + .12/2)2 – 1

12.36%

Quarterly = (1 + .12/ 4) 4 – 1

12.56%

Monthly = (1 +.12/12) 12 -1

12.68%

Daily = (1+ .12/365)365 – 1

12.747%

5. Suppose that on January 1 you deposit $100 in an account that pays a nominal (or quoted) interest rate of 11.33463%, with interest added (compounded) daily. How much will you have in your account on October 1, or 9 months later?

FV = PV (1 + i)n

PV = $100

I = 11.33463%

N= 9 months

Putting values in the formula we get FV

100 (1 + .1133463/365).75 * 365

100 1`(1.0887)

$108.87

Use the following information for Questions 6 and 7:

A firm issues a 10-year, $1,000 par value bond with a 10% annual coupon and a required rate of return is

10%.

6. What would be the value of the bond described above if, just after it had been issued, the expected inflation rate rose by 3 percentage points, causing investors to require a 13% return? Would we now have a discount or a premium bond?

V= PV of Interest payments + PV of Maturity value of bond

V= 100 * [1-1/ (1+.13)10]/.13 + 1000/(1.13)10

542.6 + 294.58

$837

The intrinsic value 837<1000 so it’s a discount bond.

7. What would happen to the bond’s value if inflation fell and rd declined to 7%? Would we now have a premium or a discount bond?

V= PV of interest payments + PV of maturity value of bond

V= 100 * [1-1/ (1+.07)10]/.07 + 1000/ (1.07)10

100 (7.02358) + 1000/1.967

702 + 508.349

$1210

The value 1210>1000 so it’s premium bond.

8. What is the yield to maturity on a 10-year, 9% annual coupon, $1,000 par value bond that sells for $887.00? That sells for $1,134.20? What does a bond selling at a discount or at a premium tell you about the relationship between rd and the bond’s coupon rate?

YTM=Kdl+ [(Kdl- Kdh)(PVl-PVytm)]/PVl-PVh

.09+ [(.12 - .09)(1000-887)]/(1000-830.47)

.09+ 3.39/169.53

10.99%

If market price =1134.20 YTM=?

Using the same procedure we will calculate YTM as follow:

If Kd=9% then V=1000<1134.20

If Kd= 7% then V= 90[1-1/ (1.07)10]/.07 + 1000/1.0710

632 + 508.3

1140> 1134

Putting the formula YTM= .07 + [ (.09-.07)(1140-1134.20)]/(1140-1000)

7.08285%

When Kd = coupon rate Then bond will have value equal to face value of bond

When Kd > coupon rate then bond will be selling at discount

When Kd < coupon rate bond will be selling at premium

9. What are the total return, the current yield, and the capital gains yield for the discount bond in Question #8 at $887.00? At $1,134.20? (Assume the bond is held to maturity and the company does not default on the bond.)

Current yield of the bond= annual coupon payment/ market price of the bond

In the current question Current yield will be: 90/887 = 10.146%

YTM = current yield + capital Gain yield

10.99%= 10.146 + x

X= 0.843%

If market price = 1134.20 then

Current yield = 90/1134.20

7.9%

YTM = Current yield + Capital Gain yield

1. Capital Gain yield = 0.855%