AGEC $424$
Answer key Chapter 5 homework (these are 5th edition problem numbers)
4. Nu-Mode Fashions Inc. manufactures quality women’s wear, and needs to borrow money to get through
a brief cash shortage. Unfortunately, sales are down, and lenders consider the firm risky. The CFO has
asked you to estimate the interest rate Nu-Mode should expect to pay on a one year loan. She’s told you to
assume a 3% default risk premium even though the loan is relatively short, and to assume the liquidity and
maturity risk premiums are each ½%. Inflation is expected to be 4% over the next twelve months.
Economists believe the pure interest rate is currently about 3½%.
Solution: Write the interest rate model and substitute. Since the loan is for one year, the inflation
adjustment is simply the expected inflation rate for the year.
k = kpr + INFL + DR + LR + MR
k = 3.5 + 4.0+ 3.0 + .5 + .5
k = 11.5%
5. Calculate the rate Nu-Mode in the last problem should expect to pay on a two year loan. Assume a 4%
default risk premium and liquidity and maturity risk premiums of ¾% due to the longer term. Inflation is
expected to be 5% in the loan’s second year.
Solution: First calculate the inflation premium as the average inflation rate over the life of the loan.
INFL = (4 + 5)/2 = 4.5%
Then write the interest rate model and substitute.
k = kpr + INFL + DR + LR + MR
k = 3.5 + 4.5+ 4.0 + .75 + .75
k = 13.5%
7. Adams Inc. recently borrowed money for one year at 9%. The pure rate is 3%, and Adams’ financial
condition warrants a default risk premium of 2% and a liquidity risk premium of 1%. There is little or no
maturity risk in one-year loans. What inflation rate do lenders expect next year?
Solution: Use the interest rate model to calculate the inflation adjustment.
k = kpr + INFL + DR + LR + MR
9 = 3 + INFL + 2 + 1 + 0
INFL = 3%
Since the loan is for one year, the inflation adjustment equals the expected inflation rate for the year.
12. Inflation is expected to be 5% next year and a steady 7% each year thereafter. Maturity risk premiums
are zero for one year debt but have an increasing value for longer debt. One-year government debt yields
9% whereas two-year debt yields 11%.
a. What is the real risk-free rate and the maturity risk premium for two-year debt?
b. Forecast the nominal yield on one- and two-year government debt issued at the beginning of
the second year.
SOLUTION:
a. For one-year government debt
k1 = kPR + I1 + MR1
9% = kPR + 5% + 0%
kPR = 4%
Then for two-year government debt
k2 = kPR + (I1+I2)/2 + MR2
11% = 4% + 6% + MR2
MR2 = 1%
b.
k1 = kPR + I2
= 4% + 7% = 11%
k2 = kPR + (I2 + I3)/2 + MR2
= 4% + 7% +1%
= 12%