1. The real risk free rate of return is currently 1.5%.Inflation is expected to
ID: 2644077 • Letter: 1
Question
1. The real risk free rate of return is currently 1.5%.Inflation is expected to be 2% the next two years and 3% the following year.If the Maturity Risk Premium is .5% what is the yield on a 3 year treasury security?(be sure to show your calculation)
2. Delta Corporation bond pays an annual coupon rate of 7% with 4 years remaining until maturity. The par value of the bond is $1,000. Determine the current market value of the bond if the yield to maturity is 8%. (Be sure to indicate your inputs to the financial calculator)
N I/YR PV PMT FV
Explanation / Answer
Part 1:
The formula for calculating yield on treasury securities is:
r = r + IP + MRP, where r is the real risk free rate, IP is the inflation premium and MRP is the maturity risk premium.
Since, we have to calculate the yield for 3 years treasury security, we will have to calculate the inflation premium for 3 years with the use of following formula:
IP = (Expected Inflation for Year 1 + Expected Inflation for Year 2 + Expected Inflation for Year 3)/3
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Solution:
Using the values provided in the question and above formulas, we get,
Inflation Premiun = (2 + 2 + 3)/3 = 2.33
3 Year Yield on Treasury Security (r) = 1.5 + 2.33 + .5 = 4.33%
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Part 2:
The function/formula that can be used to calculate the market value with the use of financial calculator would be PV(I/YR,N,PMT,FV) where I/YR = Yield to Maturity, N = Period, PMT = Coupon Amount, FV is Face Value and PV is the Present (Market) Value of the Bond.
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Solution:
Here, I/YR = 8%, N = 4 Years, PMT = 1,000*7% = 70, FV = 1000 and PV=?
Using the above value in the present value function, we get,
Market Value = PV(8%,4,70,1000) = $966.88
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