A newly issued 20-year maturity, zero-coupon bond is issued with a yield to matu

Question

A newly issued 20-year maturity, zero-coupon bond is issued with a yield to maturity of 8.2% and face value $1,000. Find the imputed interest income in the first, second, and last year of the bond's life. (Do not round intermediate calculations. Round your answers to 2 decimal places.) The yield to maturity on one-year zero-coupon bonds is 8%. The yield to maturity on two-year zero-coupon bonds is 9%. What is the forward rate of interest for the second year? (Do not round intermediate calculations. Round your answer to 2 decimal places.) If you believe in the expectations hypothesis, what is your best guess as to the expected value of the short-term interest rate next year? (Do not round intermediate calculations. Round your answer to 2 decimal places.) If you believe in the liquidity preference theory, is your best guess as to next year's short-term interest rate higher or lower than in (b)? Lower Higher

Explanation / Answer

Answer (7)

Imputed interest

First year       = $ 82.00

Second year = $ 88.71

Last year       = $ 366.55

Par Value = $ 1,000

Time to maturity = 20 years

Yield to maturity = 8.2% or 0.082

Imputed interest income for first year = Acqusition price for the year * ytm = $ 1000 * 0.082

                                                                      = $ 82.00

Imputed interest income for second year = (Initial price + imputed interst for first year) * ytm

                                                                          = (initial price * (1+ytm)^n-1) * ytm

                                                                         = (1000 * (1+0.082)^2-1)*ytm

                                                                         = 1000*1.082*0.082          

                                                                          = $ 88.724 or $ 88.72

Imputed interest income for last year = (initial price + imputed interest for 19 years) * ytm

                                                                    = (1000 * 1.082^19) * 0.082

                                                                    = $ 366.5488 or $ 366.55 (rounded off)

Answer (10)

(a)Forward rate of interest = 10.01%

(b)Best guess for value of short term interest rate next year = 10.01%

(c)Based on the liquidity preference theory, the next year short term interest rate would be higher than the current year

YTM on one year zero coupon bond = 8% or 0.08

YTM on two year zero coupon bond = 9% or 0.09

Forward rate is the rate at which one can invest proceeds of a one year zero coupon bond after maturity in a one year zero coupon bond so that the same is equal to investing in a two year zero coupon bond.

Let r be the forward interest rate on a one year zero coupon bond one year from now. Then

(1+0.08) * (1+r) = 1+0.09)^2

1.08 * (1+r) = 1.1881

1+r = 1.1881/1.08 = 1.1000929

r = 1.1000929 – 1 = 10.009 or 10.01% (rounded off)

Based on the expectations hypothesis, the above rate of 10.01% is the best guess for the short term interest rate one year from now.

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