Question

6-12 Personal Finance Problem Valuation fundamentals Imagine that you are trying to evaluate the economics of pur- chasing an automobile. You expect the car to provide annual after-tax cash benefits of $1,200 at the end of each year and assume that you can sell the car for after-tax proceeds of $5,000 at the end of the planned 5-year ownership period. All funds for purchasing the car will be drawn from your savings, which are currently earning 6% after taxes. a. Identify the cash flows, their timing, and the required return applicable to valuing the car. b. What is the maximum price you would be willing to pay to acquire the car? Explain.

Answer 1

a. cash flows and their timing:

year	cash flow
1	1200
2	1200
3	1200
4	1200
5	(1200+5000)=>6200

The appropriate discount rate will be 6%

b.maximum price to be paid for the car = present value of cash flows:

since 1200 is received for 5 years as annuity , its present value can be known using present value of annuity factor

=>A*[1-(1+r)^(-n)]/r

=>1200*[1-(1.06)^(-5)]/0.06

=>1200*4.21236333

=>$5,054.84.

present value of terminal cash flow of $5000

=>5000*1/(1+r)^n.

=>5000* 1 /(1.06)^5.

=>$3,736.29.

maximum price to be paid for the car = 5054.84+3736.29

=>$8,791.13.