Question

what discount rate would make you infifferent between receiving $3561 per year forever and $5640 per year for 23 years? Assume the first payment of both cash flow strams occur in one year

Answer 1

Present value of Annuity = Present value of perpetuity

PV of Annuity = Cash Flow * [ 1 - [(1+r)^-n]] /r
PV of perpetuity = Annual cash flows(cf)/discount rate(r)
r = Int rate per period
n = No. of periods
Cash Flow * [ 1 - [(1+r)^-n]] /r = Annual cash flows(cf)/discount rate(r)
$5640[1-(1+discount rate)^-23]/discount rate = $3561/discount rate
$5640[1-(1+discount rate)^-23] = $3561
[1-(1+discount rate)^-23] = ($ 3561/ $ 5640)
[1-(1+discount rate)^-23]=0.6313
1/(1+discount rate)^23 =0.3687
1+discount rate=(1/ 0.3686) ^ (1/23)
1+discount rate = (2.712) ^ (1/23)
1+discount rate = 1.04433
Discount rate = 0.04433
Discoiunt rate = 4.433 %

Please comment if any assistane is required