Question

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From discussions with your broker, you have determined that the expected inflation premium is 1.35 percent...

From discussions with your broker, you have determined that the expected inflation premium is 1.35 percent next year, 1.50 percent in year 2, 1.75 percent in year 3, and 2.00 percent in year 4 and beyond. Further, you expect that real risk-free rates will be 3.20 percent next year, 3.30 percent in year 2, 3.75 percent in year 3, and 3.80 percent in year 4 and beyond. You are considering an investment in either five-year Treasury securities or five-year bonds issued by PeeWee Corporation. The bonds have no special covenants. Your broker has determined the following information about economic activity and PeeWee Corporation five-year bonds:

Default risk premium = 2.10%

Liquidity risk premium = 1.75

Maturity risk premium = 0.75

Further, the maturity risk premium on PeeWee bonds is 0.1875 percent per year starting in year 2. PeeWee’s default risk premium and liquidity risk premium do not change with bond maturity.

  1. What is the fair interest rate on five-year Treasury securities?
  2. What is the fair interest rate on PeeWee Corporation five-year bonds?
  3. Plot the five-year yield curve for the Treasury securities.
  4. Plot the five-year yield curve for the PeeWee Corporation bonds.

Solutions

Expert Solution

a. What is the fair interest rate on five year treasury security?

Sol:- As treasury security is being issued by the government, there is no default risk because in finance we believe that government can not default, as they have the ability to print the currency and repay the debt.

Liquidity premium is the overhead charged by the issuer if the instrument is not very liquid or do not get converted in to cash very frequently at its fair value, so the investor asks for the additional premium to compensate this loss.

based on the data given in the above question:

Face value $100
Default risk premium 2.10%
Liquidity risk premium 1.75%
Maturity risk premium 0.75%

Following are the required calculation to get the desired data:-

Year 1 2 3 4 5
Inflation Premium 1.35% 1.50% 1.75% 2% 2%
Real Risk free rates 3.20% 3.30% 3.75% 3.80% 3.80%
Liquidity risk premium 1.75% 1.75% 1.75% 1.75% 1.75%
Maturity risk premium 0.75% 0.75% 0.75% 0.75% 0.75%
Fair Interest Rate(Addition) 7.05% 7.30% 8.00% 8.30% 8.30%
Future Value 107.05 115.13 125.97 137.57 148.98

YTM =8.30%

b. What is the fair interest rate on Pee Wee Corporation five year bonds?

Soln:-

Face value $100 Assumption
Default risk premium 2.10%
Liquidity risk premium 1.75%
Maturity risk premium 0.75%

Calculation of fair interest rate

Year 1 2 3 4 5
Inflation Premium 1.350% 1.500% 1.750% 2.000% 2.000%
Real Risk free rates 3.200% 3.300% 3.750% 3.800% 3.800%
Liquidity risk premium 1.750% 1.750% 1.750% 1.750% 1.750%
Maturity risk premium 0.750% 0.188% 0.188% 0.188% 0.188%
Default risk premium 2.100% 2.100% 2.100% 2.100% 2.100%
Fair Interest Rate 9.150% 8.838% 9.538% 9.838% 9.838%
Future Value 109.15 118.46 131.43 145.55 159.86

YTM will be 9.84%

c. Five year Yield curve of treasury security.

Soln:-

Year 1 2 3 4 5
YTM 7.05% 6.74% 7.44% 7.74% 7.74%

c. Five year Yield curve of PeeWee Corporation

Year 1 2 3 4 5
YTM 9.15% 8.84% 9.54% 9.84% 9.84%

.

jeff jeffy answered 9 months ago
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