Question

Consider an investment that will pay you $1,000 each year for five years. After that, the payment will grow by 3 percent per year indefinitely, so that the payment in year 6 will be $1,030, the payment in year 7 will be $1,060.90, and so forth.

If your required rate of return on this investment is 13 percent, what is the most you’d be willing to pay for it?

If the investment costs you $8,000 today, what is its net present value?

Answer 1

PV OF ALL CASHFLOWS = a X PVIFA @i% FOR n YEARS + PV OF GROWING PERPETUITY

PV OF ALL CASHFLOWS = a X PVIFA @i% FOR n YEARS + [a/ (i-g)] x PVIF @ i%, 5 years

PV OF ALL CASHFLOWS = $1000 X PVIFA @13% FOR 5 YEARS + [$1030/ (0.13-0.03)] x PVIF @ 13%, 5 years

PV OF ALL CASHFLOWS = ($1000 X 3.5172) + ($10300 x 0.543) =$3517.2 + $5592.9 = $9110.1

$9110.1 = this is the amount you wpuld be willing to pay

If investment costs you $8000 today,

NPV = PV OF ALL CFAT - INVESTMENT = $9110.1 -$8000 = 1110.1

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