Finance 415

Corporate Finance Assignment 3 Due Monday, February 26th at the beginning of class at TA’s office (Lezgin Ay, Room 4112) Class number: Name: ID: Note: Show all work in a clear manner. Print your work if you work in excel. Question 1

Maturity Years to Maturity Ask Price Calculated Yield 5/15/2013 1 99.883 0.001171371 5/15/2014 2 99.387 0.003079164 5/15/2015 3 98.606 0.004690323 5/15/2016 4 97.163 0.007220998 5/15/2017 5 95.412 0.00943742 5/15/2018 6 93.143 0.011909399 5/15/2019 7 90.282 0.014711751 5/15/2020 8 86.905 0.017699133 5/15/2021 9 83.735 0.019919479 5/15/2022 10 80.612 0.021786194

Using the Strips price data above, calculate the yields for 1-year to 10-year Strips, in 1-year increments. Assume today is May 15th, 2012. Report the graph with yield on the y-axis and years to maturity on the x-axis. How do you interpret the current yield curve? Question 2

Suppose you work at an investment bank and want to construct a bond with a 4-year maturity and 8% coupon payments (paid annually), and a $1,000 face value. Your will assume that your firm’s bonds are riskless, and thus you can base the bond’s discount rates on U.S. Treasury Notes.

Maturity Years to Maturity Ask Price Coupon 4/30/2013 1 100.4453 0.625 4/30/2014 2 103.2031 1.875 4/30/2015 3 106.2422 2.5 4/30/2016 4 107.8594 2.625

Using the above “Treasury Quotes”, calculate the price at which your bond should sell. You will

have to calculate four different yields to use as the discount rates. Show how you calculated each yield. Assume today is April 30th, 2012. For simplicity, also assume that the Treasury Notes pay coupons annually.

Hint: you need Bootstrapping to calculate the yields at different maturities. For the one-year yield, you can use the formula 𝑃𝑃1 =

𝐶𝐶1+𝐹𝐹𝐹𝐹 1+𝑟𝑟1

, where you plug in 𝑃𝑃1 = 100.4453,𝐶𝐶1 = 0.625,𝐹𝐹𝐹𝐹 = 100, and

you can get 𝑟𝑟1. Next, you plug in 𝑟𝑟1 as well as other variable values to 𝑃𝑃2 = 𝐶𝐶2 1+𝑟𝑟1

+ 𝐶𝐶2+𝐹𝐹𝐹𝐹 (1+𝑟𝑟2)2

to get 𝑟𝑟2. You can continue this procedure until you solve for all four yields.

Question 3 Your mining company is considering an expansion of operations into iron ore. Your engineers surveyed a particular piece of land (the survey cost $200,000) and concluded the following:

• You can extract 100,000 tons of iron ore per year. • There are 2 million tons of iron ore underneath this land (hint: 20 years’ cash flows). • As you dig deeper, the operating cost to extract the ore will increase. So assume that costs will

grow by 6.5 percent per year. The operating cost in the first year will be 6 million dollars (hint: the operating cost can be viewed as the COGS or expense).

Your business associates tell you the following additional information:

• The ore will sell for $100 per ton for the first year, and the price is forecasted to grow by 3.3 percent per year for the next 20 years.

• We can invest in the equipment for this project right now for 15 million dollars. • The equipment is depreciated straight-line over 20 years, with an assumed salvage value of zero

(hint: the annual depreciation is 15/20 = 0.75 million). Assume a constant tax rate of 40%, and an after-tax cost of capital of 10% (hint: 10% can be viewed as the discount rate for future cash flows). All numbers are nominal. You may use Solver in Excel to answer (b) and (c).

a) What is the net present value of this project? (Hint: the annual cash flow = (revenue – cost – depreciation)x(1-tax)+depreciation)

b) Suppose you are uncertain about the growth rate for the operating cost. What growth rate for the operating cost would you need in order to break even (net present value of zero) from this project?

c) Go back to assuming the original growth rate in costs. How high would the initial investment in the equipment have to be in order for you to break even from this project?