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Unformatted text preview: Problem Set #2 Bond Pricing, Term Structure and NPV Page.4 Problem Set #2 Bond Pricing, Term Structure and NPV 1. A Treasury bond has the following characteristics: • Principal: $1,000. • Term to maturity: 20 years. • Coupon rate: 8 percent. • Semiannual payments. Calculate the price of the bond if the stated annual interest rate (compounded annually) is (a) 8 percent; (b) 10 percent; (c) 6 percent. 2. You are given the following information on three traded bonds making annual coupon pay- ments. Face Yield to Bond Value Rate Maturity Maturity A $1,000 0.00% 1 year 5.00% B $1,000 5.00% 2 years 5.85% C $1,000 10.00% 2 years 6.00% (a) What are the prices of the above three bonds? (b) Is it possible to make arbitrage profits using only these three bonds? If so, give an fl ♦ arbitrage strategy (making sure that the profits are realized today). Hint: Try to solve for the discount factors. 3. A 6%, 6-year bond yields 12%, and a 10%, 6-year bond yields 8%. Calculate the 6-year spot rate r 6 . (Assume annual coupon payments for both bonds.) 4. In Figure 1, the sloping straight line represents the opportunities for investment in the capital market, and the solid curved line represents the opportunities for investment in plant and machinery (real assets). The company’s only asset at present is $2.6 million in cash. (a) What is the interest rate? (b) How much should the company invest in plant and machinery? (c) How much will this investment be worth next year? (d) What is the average rate of return on the investment? (e) What is the marginal rate of return? (f) What is the present value of this investment? (g) What is the net present value of this investment? (h) What is the total present value of the company? Problem Set #2 Bond Pricing, Term Structure and NPV Page.5 (i) How much will the individual consume today? (j) How much will he consume tomorrow? (k) Is he a borrower or a lender? 5. Casper Milktoast has $200,000 available to support consumption in periods 0 (now) and 1 (next year). He wants to consume exactly the same amount in each period. The interest rate is 8%. There is no risk. (a) How much should he invest, and how much can he consume in each period? (b) Suppose Casper is given an opportunity to invest up to $200,000 at 10% riskfree. The interest rate stays at 8%. What should he do, and how much can he consume in each period (i) if he is not allowed to borrow against future income? (ii) if he is allowed to borrow against future income? (c) What is the NPV of each opportunity in (b)?...
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This note was uploaded on 03/13/2012 for the course UGBA 103 taught by Professor Berk during the Spring '07 term at Berkeley.
- Spring '07