Problem 1

a. Current Savings Needed = $ 500,000/1.110 = 192,772 $

b. Annuity Needed = $ 500,000 (APV,10%,10 years) = 31,373 $

Problem 3

Annual Percentage Rate = 8%

Monthly Rate = 8%/12 = 0.67%

Monthly Payment needed for 30 years = $ 200,000 (APV,0.67%,360) = 1,473 $

Problem 5

a. Year-end Annuity Needed to have $ 100 million available in 10 years = 6.58 $

[FV = $ 100, r = 9%, n = 10 years]

b. Year-beginning Annuity Needed to have $ 100 million in 10 years = 6.04 $

Problem 7

Value of Stock = 1.50 (1.06)/ (.13 - .06) = 22.71 $

Problem 9

Expected Rate of Return = (1000/300)^(1/10) - 1 = 12.79%

Problem 11

Annuity given current savings of $ 250,000 and n=25 = 17,738.11 $

Problem 13

PV of deficit reduction can be computed as follows –
 

Year	Deficit Reduction	PV
1	25.00	23.15
2	30.00	25.72
3	35.00	27.78
4	40.00	29.40
5	45.00	30.63
6	55.00	34.66
7	60.00	35.01
8	65.00	35.12
9	70.00	35.02
10	75.00	34.74

Sum 500.00 $ 311.22 $

The true deficit reduction is $ 311.22 million.

Problem 15

a.
 

Year	Nominal	PV
0	$5.50	$5.50
1	$4.00	$3.74
2	$4.00	$3.49
3	$4.00	$3.27
4	$4.00	$3.05
5	$7.00	$4.99
$28.50	$24.04

b. Let the sign up bonus be reduced by X.

Then the cash flow in year 5 will have to be raised by X + 1.5 million,

to get the nominal value of the contract to be equal to $30 million.

Since the present value cannot change,

X - (X+1.5)/1.075 = 0

X (1.075 - 1) = 1.5

X = 1.5/ (1.075 -1) = $3.73 million

The sign up bonus has to be reduced by $3.73 million and the final year's cash flow has to be

increased by $5.23 million, to arrive at a contract with a nominal value of $30 million and a

present value of $24.04 million.

Problem 17

a. Monthly Payments at 10% on current loan = 1,755.14 $

b. Monthly Payments at 9% on refinanced mortgage = 1,609.25 $

Monthly Savings from refinancing = 145.90 $

c. Present Value of Savings at 8% for 60 months = 7,195.56 $

Refinancing Cost = 3% of $ 200,000 = $6,000

d. Annual Savings needed to cover $ 6000 in refinancing cost= 121.66 $

Monthly Payment with Savings = $ 1755.14 - $ 121.66 = 1,633.48 $

Interest Rate at which Monthly Payment is $ 1633.48 = 9.17%

Problem 19

a. Estimated Funds at end of 10 years:

FV of $ 5 million at end of 10th year = 10.79 $ (in millions)

FV of inflows of $ 2 million each year for next 5 years = 17.24 $

- FV of outflows of $ 3 million each year for years 6-10 = 17.60 $

= Funds at end of the 10th year = 10.43 $

b. Perpetuity that can be paid out of these funds = $ 10.43 (.08) = 0.83 $

Problem 21
 

Year	Coupon	Present Value @ 8%
1	50.00	46.30
2	50.00	42.87
3	50.00	39.69
4	50.00	36.75
5	50.00	34.03
6	60.00	37.81
7	70.00	40.84
8	80.00	43.22
9	90.00	45.02
10	100.00+1000.00	509.511
	$ Sum =	876.05