Question

Present Value of an Annuity

1) On January 1, 2016, you win $2,600,000 in the state lottery. The $2,600,000 prize will be paid in equal installments of $260,000 over 10 years. The payments will be made on December 31 of each year, beginning on December 31, 2016. If the current interest rate is 5%, determine the present value of your winnings. Use Table 2. Round to the nearest whole dollar.
$

2) Compute Bond Proceeds, Amortizing Premium by Interest Method, and Interest Expense

Evans Co. produces and sells motorcycle parts. On the first day of its fiscal year, Evans Co. issued $20,000,000 of four-year, 14% bonds at a market (effective) interest rate of 12%, with interest payable semiannually. Compute the following:

a. The amount of cash proceeds from the sale of the bonds. Use the tables of present values in Exhibit 4 and Exhibit 5. Round to the nearest dollar.
$

b. The amount of premium to be amortized for the first semiannual interest payment period, using the interest method. Round to the nearest dollar.
$

c. The amount of premium to be amortized for the second semiannual interest payment period, using the interest method. Round to the nearest dollar.
$

d. The amount of the bond interest expense for the first year. Round to the nearest dollar.
$

Answer 1

The Table 2 and Exhibit 4 and Exhibit 5 are not given. As such it is not known whether to use PV factors upto 4 decimals or upto 5 decimals.

Two sets of answers are given.

Part 1 Assuming PV factors upto 4 decimals:

Answer 1:

Annuity paid at the end of each year (Ordinary annuity) = $260,000,

Time period = 10 years

PV factor of annuity of $1 for 10 years with discount rate of 5% = 7.7217

Present value of your winnings = 260000 * 7.7217 = $2,007,642

Present value of your winnings = $2,007,642

Answer 2 (a):

Bond par value = $20,000,000

Semiannual coupon = 20000000 * 14%/2 = $1,400,000

Semiannual Market interest rate = 12% / 2 =6%

Time to maturity = 4 * 2 = 8 semiannual periods

Cash proceeds from the sale of the bonds = Semiannual coupon * PV factor of Annuity of $1 for 8 years at 6 % discount + Par value * PV factor of $1 for 8 periods at 6% discount

= 1400000 * 6.2098 + 20000000 * 0.6274

= $21,241,720

Cash proceeds from the sale of the bonds = $21,241,720

Answer 2 (b):

First semiannual interest payment period:

Interest Expense = 21241720 * 6% = $1,274,503.20

Amount of premium to be amortized = Cash paid - Interest expense = 20000000 * 14%/2 - 1274503.20 = $125,496.80

Amount of premium to be amortized = $125,497

Answer 2 (c):

Second semiannual interest payment period = 1400000 - (21241720 - 125496.80) * 6% =$133,026.61

Second semiannual interest payment period = $133,027

Answer 2 (d):

Amount of the bond interest expense for the first year = 21241720 * 6% + (21241720 - 125496.80) * 6% = $2,541,476.59

Amount of the bond interest expense for the first year = $2,541,477

Assuming PV factors upto 5 decimals:

Answer 1:

Annuity paid at the end of each year (Ordinary annuity) = $260,000,

Time period = 10 years

PV factor of annuity of $1 for 10 years with discount rate of 5% = 7.72173

Present value of your winnings = 260000 * 7.72173 = $2,007,649.80

Present value of your winnings = $2,007,649.80

Answer 2 (a):

Bond par value = $20,000,000

Semiannual coupon = 20000000 * 14%/2 = $1,400,000

Semiannual Market interest rate = 12% / 2 =6%

Time to maturity = 4 * 2 = 8 semiannual periods

Cash proceeds from the sale of the bonds = Semiannual coupon * PV factor of Annuity of $1 for 8 years at 6 % discount + Par value * PV factor of $1 for 8 periods at 6% discount

= 1400000 * 6.20979 + 20000000 * 0.62741

= $21,241,906

Cash proceeds from the sale of the bonds = $21,241,906

Answer 2 (b):

First semiannual interest payment period:

Interest Expense = 21241906 * 6% = $1,274,514.36

Amount of premium to be amortized = Cash paid - Interest expense = 20000000 * 14%/2 - 1274514.36 = $125,485.64

Amount of premium to be amortized = $125,486

Answer 2 (c):

Second semiannual interest payment period = 1400000 - (21241906 - 125485.64) * 6% = $133,014.78

Second semiannual interest payment period = $133,015

Answer 2 (d):

Amount of the bond interest expense for the first year = 21241906 * 6% + (21241906 - 125485.64) * 6% = $2,541,499.58

Amount of the bond interest expense for the first year = $2,541,500