Question

A bond has a 10 percent coupon rate, makes annual payments, matures in 12 years, and has a yield-to-maturity of 7 percent.

1. Eleven years from now the bond will have 1 year until maturity. Assume market interest rates are at 7 percent, the same place they were when the bond was issued. Given this: k. What will be the bond’s price 11 years from now? l. What will be the current yield eleven years from now? m. What is the expected capital gains yield eleven years from now? n. How does you answers to part (l) and (m) compare with your answers to parts (b) and (c)?

2. Your client’s daughter recently inherited some bonds (face value $50,000) from her father. She wants to cash the bonds in and place the proceeds into an account paying 7 percent compounded annually. The three percent annual coupon bonds mature on October 19th, 2035, and it is now October 19th, 2020. The bonds have a current yield-to-maturity of 5 percent. She wants to make three equal, annual withdrawals from the account, with the first withdrawal occurring today the third payment two years from today. Upon the third withdrawal, the account balance will be zero. What is the largest amount she could withdraw for three years, beginning today?

Answer 1

(Following chegg guidelines in case a student ask for multiple questions we can solve only one question. i am solving question 2 because 1st question is incomplete (part b and c are missing). please consider)

2)

first we have to calculate value of bond today

value of bond = present value of future cash flows diacounted at YTM

coupons = 50,000*3% = 1500

number of periods = 15

value of bond = 1500*PVIFA(r = 5% ; n = 15) + 50,000*PVF(r = 5% ; n = 15)

= 1500*10.37966 + 50,000*0.48102

= $39,620.34

(PVIFA = [1 - (1+r)^-n / r ] ; PVF = 1 / (1+r)^n )

Present value of annuity due = P*[1 - (1+r)^-n / r ]*(1+r)

r = rate of interest = 7%

n = number of periods

p = annual withdrawls

39,620.34 = P*[1 - (1+7%)^-3 / 7%]*(1+7%)

P = 39,620.34 / 2.8080182

so largest amount = $14,109.72