Question

Sherwin Williams will receive $20,650 a year for the next 20 years as a result of a picture he has painted. Use Appendix D for an approximate answer, but calculate your final answer using the formula and financial calculator methods a. What is the present value of these payments if the discount rate is 7 percent? (Do not round intermediate calculations, Round your final answer to 2 decimal places.) Present value b. Should he be willing to sell out his future rights now for $173,000 Yes No

Answer 1

Let's compute the PV of all such future payments and compare this PV with $173,000 to
assess if so calculated PV is greater than $173,000.
PV of annuity
P = PMT x (((1-(1 + r) ^- n)) / r)
Where:
P = the present value of an annuity stream	To be computed
PMT = the dollar amount of each annuity payment	$                           20,650.00
r = the effective interest rate (also known as the discount rate)	7.00%
n = the number of periods in which payments will be made	20
PV of first annuity=	PMT x (((1-(1 + r) ^- n)) / r)
PV of first annuity=	20650* (((1-(1 + 7%) ^- 20)) / 7%)
PV of first annuity=	$                         218,766.39
Since PV of future benefits is $ 218,766.39 which is higher than the price being offered of $ 173,000 hence
it is suggested not to sell future rights.