 ## Applied Corporate Finance

IBM Thomas J. Watson Research Center

Prof. Ian Giddy

E-mail: ian.giddy@nyu.edu Web: www.giddy.org
Course Web site: giddy.org/ibmfinance

Time Value of Money:

Suggested Solutions

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

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

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