Question

Bill Preston has signed a contract that will pay him $55,000 at the beginning of each year for the next 7 ​years, plus an additional $110,000 at the end of year 7.

If 12% is the appropriate discount​ rate, what is the present value of this​ contract?

Answer 1

Since the payment will be received at the beginning of each year for the next 7 years, First payment will be received at the beginning of Year 1 and second payment will be received at the beginning of Year 2, that is at the end of Year 1

So, Cash flows from Year 2 to Year 7 will be discounted as per the following table with PV Factor for year 1 being used for cash flow for year 2 and like wise all cash flows will be discounted

PV Factor

= 1 / (1 + r) ^ n

Where,

r = 12% or 0.12

n = 1 to 7

So, PV Factor for year 2

= 1 / (1.12^2)

= 1 / 1.2544

= 0.797193

Calculations		A	B	C = A x B
Year	Payment time	Payment	PV Factor	Present Value
0	Beginning of Year 1	55000	1.000000	55,000.00
1	Beginning of Year 2	55000	0.892857	49,107.14
2	Beginning of Year 3	55000	0.797194	43,845.66
3	Beginning of Year 4	55000	0.711780	39,147.91
4	Beginning of Year 5	55000	0.635518	34,953.49
5	Beginning of Year 6	55000	0.567427	31,208.48
6	Beginning of Year 7	55000	0.506631	27,864.71
7	End of Year 7	110000	0.452349	49,758.41
	Present Value of contract			330,885.82