Applied Corporate Finance
Prof. Ian Giddy Email: 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. Yearend Annuity Needed to have $ 100 million available in 10 years = 6.58 $ [FV = $ 100, r = 9%, n = 10 years] b. Yearbeginning 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 –
The true deficit reduction is $ 311.22 million.
Problem 15 a.
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 610 = 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
