Question

a. Keenan Industries has a bond outstanding with an 8.25% coupon, payable semiannually, and a $1,000 par value. The bond's dollar price is $1,066.00 and the bond is callable at 104. The bond's yield to call is 7.41 percent. When can the bond be called (round to the nearest whole year)?

b. You turn 35 today, and you plan to save $2,000 each month for retirement, with the first deposit made at the end of this month. You plan to retire 30 years from today, when you turn 65, but you're not sure how long you can expect to live after retirement, so you want the payments to go on forever. Under these assumptions, how much can you spend each month after you retire? Your first withdrawal will be made at the end of the first month of retirement.

c. You agree to make 36 deposits of $750 at the end of each month into a bank account. At the end of the 36th month, you will have $30,000 in your account. If the bank compounds interest monthly, what nominal annual interest rate will you be earning?

You will invest in a mutual fund that's expected to provide a return of 4.5% per year, compounded monthly throughout your life.

Answer 1

a]

Years to maturity is calculated using NPER function in Excel :

rate = 7.41%/2 (converting annual YTC to semiannual YTC)

pmt = 1000*8.25%/2 (semiannual coupon payment = face value * coupon rate / 2)

pv = -1066 (current bond price. This is entered with a negative sign because it is a cash outflow to the buyer of the bond today)

fv = 1040 (call price = face value * 104% = $1,000 * 104% = $1,040)

The NPER calculated is the number of semiannual periods until call date. To get number of years, we divide by 2.

Number of years until call date = 6 years

b]

First, we calculate the amount accumulated 30 years from today.

Future value of annuity = P * [(1 + r)n - 1] / r,

where P = periodic payment. This is $2,000

r = periodic rate of interest. This is (4.5%/12). We divide by 12 since we need to convert the annual rate into monthly rate)

n = number of periods. This is 30 * 12 = 360

Future value of annuity = $2,000 * [(1 + (4.5%/12))360 - 1] / (4.5%/12)

Future value of annuity = $1,518,772.29

Present value of perpetuity = perpetual periodic payment / periodic interest rate

$1,518,772.29 = perpetual periodic payment / (4.5%/12)

perpetual periodic payment = $5,695.40

You can spend $5,695.40 each month after you retire

c]

nominal annual rate is calculated using RATE function in Excel :

nper = 36 (total number of monthly deposits)

pmt = -750 (Monthly deposit. This is entered with a negative sign because it is a cash outflow)

pv = 0 (beginning amount in account is zero)

fv = 30000 (ending value of account)

The RATE calculated is the nominal monthly rate. To get nominal annual rate, we multiply by 12.

nominal annual rate is 7.12%

nominal annual rate is 7.12%