Assume that you own a hundred $1,000 par value bonds,with a total face value of $100,000.These bonds have a 4 percent coupon,pay interest semiannually,and have 5 years remaining until they mature.New bonds with the same risk and maturity provide yields to maturity of 14 percent.You are considering selling your bonds and depositing the proceeds in a savings account which pays interest at a rate of 6 percent,annual compounding.If you do make the transaction,you will liquidate the savings account by making 5 equal withdrawals,the first coming 1 year from now.What will be the amount of each annual withdrawal?
A) $12,940
B) $15,403
C) $24,860
D) $29,425
E) $64,880

Question

Quizplus · Accepted Answer

To find the amount of each annual withdrawal, we first need to calculate the present value of the bonds at the new yield to maturity of 14%, and then find the equivalent annual withdrawals from this amount at a 6% savings account interest rate.1. Calculate the present value of the bonds:   - The coupon payment is 4% of $1,000 = $40, but since it's semiannual, each payment is $20.   - There are 10 semiannual periods left (5 years * 2).   - The new yield to maturity is 14% annually, or 7% semiannually.The present value of the bonds can be calculated using the formula for the present value of an annuity (for the coupon payments) plus the present value of a lump sum (for the par value at maturity). The formula for the present value of an annuity is $PV = PMT \times \left(1 - \frac{1}{(1 + r)^n}\right) / r$, and for a lump sum, it's $PV = \frac{FV}{(1 + r)^n}$, where PMT is the payment per period, r is the interest rate per period, n is the number of periods, and FV is the future value.- Present value of the coupon payments: $PV_{coupons} = 20 \times \left(1 - \frac{1}{(1 + 0.07)^{10}}\right) / 0.07 \approx 138.51$ per bond.- Present value of the par value: $PV_{par} = \frac{1000}{(1 + 0.07)^{10}} \approx 508.35$ per bond.- Total present value per bond: $138.51 + 508.35 = 646.86$.- Since there are 100 bonds, the total present value is $646.86 \times 100 = 64,686$.2. Calculate the annual withdrawal amount:   - Now, we need to find the equivalent annual withdrawals from $64,686 at a 6% interest rate over 5 years.   - We use the formula for the present value of an annuity, solving for PMT this time: $PMT = PV \times \frac{r}{1 - \frac{1}{(1 + r)^n}}$, where PV is the present value, r is the annual interest rate, and n is the number of years.$PMT = 64686 \times \frac{0.06}{1 - \frac{1}{(1 + 0.06)^5}} \approx 15,403$.Therefore, the amount of each annual withdrawal would be approximately $15,403.

Assume That You Own a Hundred $1,000 Par Value Bonds,with