CorporateFinance版答案Ch.docVIP

PAGE  B-PAGE 51 Chapter 4: Net Present Value 4.32．Set the price of the note equal to the present value of the annuity of $2,000 per year. P = C ATr $12,800 = $2,000 A10r The problem can be solved by using a calculator to find the appropriate discount rate. = A10r 0.090626 = r The problem can also be solved by using table A.2 in the back of the textbook. In table A.2, scan across the row for 10-year annuity factors until one approximates 6.4. 6.4177, corresponding to a rate of 9%, is close to the above factor, 6.4. Thus, the rate received is slightly more than 9%. The rate received is 9.0626%. 4.33．a. To calculate the necessary annual payments, first find the PV of the $25,000 which you will need in five years. PV = C5 / (1+r)5 = $25,000 / (1.07)5 = $17,824.65 Next, compute the annuity that will yield the same PV as calculated above. Solve for the deposit you will make each year. PV = C ATr $17,824.65 = C A50.07 $17,824.65 / A50.07 = $4,347.27 Depositing $4,347.27 into the 7% account each year will provide $25,000 five years from today. The lump sum payment must be the present value of the $25,000 you will need five years from today. PV = C5 / (1+r)5 = $25,000 / (1.07)5 = $17,824.65 You must deposit $17,824.65 as a lump sum to have $25,000 in the account at the end of five years. 4.34．First, determine the balance of the loan Nancy must pay. Balance = $120,000 (0.85) = $102,000 Apply the annuity formula since Nancy will pay the balance of the loan in 20 equal, end-of-year, payments. Set the present value of the annuity equal to the balance of the loan. Solve for the annual payment, C. Balance = C ATr $102,000 = C A200.1 $102,000 / A200.1 = C $11,980.88 = C The equal installments are $11,980.88. 4.35．a. The cash flows form a 31-year annuity where the first payment is received today. Remember to use the after-tax cash flows. The first payment of a standard annuity is received one year from today. There