Corporate finance - solutions for chapter 6

Chapter 6
Interest Rates

Solutions to End-of-Chapter Problems



6-1 a. Term Rate
6 months 5.1%
1 year 5.5
2 years 5.6
3 years 5.7
4 years 5.8
5 years 6.0
10 years 6.1
20 years 6.5
30 years 6.3


b. The yield curve shown is an upward sloping yield curve.

c. This yield curve tells us generally that either inflation is expected to increase or there is an increasing maturity risk premium.

d. It would make sense to borrow long term because each year the loan is renewed interest rates are higher. This exposes you to rollover risk. If you borrow for 30 years outright you have locked in a 6.3% interest rate each year.


6-2 T-bill rate = r* + IP
5.5% = r* + 3.25%
r* = 2.25%.


6-3 r* = 3%; I1 = 2%; I2 = 4%; I3 = 4%; MRP = 0; rT2 = 6%; rT3 = 6.33%



6-4 rT10 = 6%; rC10 = 8%; LP = 0.5%; DRP = 1.5%



6-5 r* = 3%; IP2 = 3%; rT2 = 6.2%; MRP2 = 0.2%


6-6 r* = 5%; I1-4 = 16%; MRP = DRP = LP = 0; r4 = 21.8%.

6-7 rT1 = 5%; 1rT1 = 6%; rT2 = 5.5%.


6-8 X = 8.5%.


6-9 rT7 = 6.8%.
6-1 I = 6%.

6-11 DRP = 1.55%.


6-12 MRP5 – MRP3 = 0.75% – 0.40% = 0.35%.
6-13 DRP8 = 1.775%.
6-14 a. X = 6%.

b. For riskless bonds under the expectations theory, the interest rate for a bond of any maturity is
rN = r* + average inflation over N years. If r* = 1%, we can solve for IPN:
Year 1: r1 = 1% + I1 = 3%;
I1 = expected inflation = 3% – 1% = 2%.

Year 2: r1 = 1% + I2 = 6%;
I2 = expected inflation = 6% – 1% = 5%.

Note also that the average inflation rate is (2% + 5%)/2 = 3.5%, which, when added to r* = 1%, produces the yield on a 2-year bond, 4.5%. Therefore, all of our results are consistent.

6-15 7% = I2.
6-16 0.14 = I.
6-17 rC5 = 3.9% + 1.3% + 2%
= 7.2%.