1. Nico Nelson, a management trainee at a large New York-based bank is trying to
ID: 2761694 • Letter: 1
Question
1. Nico Nelson, a management trainee at a large New York-based bank is trying to estimate the real rate of return expected by investors. He notes that the 3-month T-bill currently yields 3 percent and has decided to use the consumer price index as a proxy for expected inflation. What is the estimated real rate of interest if the CPI is currently 2 percent?
2. What is the approximate yield to maturity for a $1,000 par value bond selling for $1,120 that matures in 6 years and pays 12 percent interest annually?
Explanation / Answer
1. Real Rate of Return = [(1+Risk Free Rate)/(1+Inflation Rate)] - 1 = (1.03 / 1.02) - 1 = 0.9804% 2. Price of Bond = [C [1 - (1+r)^-t] / r] + [F / (1+r)^t] C - Coupon Payment r - YTM F - Face Value t - Years Since, the bond is selling at premium yield is lower than coupon rate 1120 = [120 * [1 - (1+r^-6)/r] + [1000 / 1+r^6] Calculating Price at 10% = 120 * (1 - 1.1^-6/0.10) + (1000/1.1^6) = $522.63 + 564.47 = $1087.10 which is less than $1120. This implies that yield is below 10% Calculating Price at 9% = 120 * (1 - 1.09^-6/0.09) + (1000/1.09^6) = $538.31 + 596.27 = $1134.58 Using Interpolation techinque, YTM = 9% + (1120 - 1134.58) / (1087.10 - 1134.58) * (10-9) = 9% + 14.5776/47.4723 = 9.31%
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