Question

Year 1 $50

Year 2-6: 4% more than the previous year

Year 7 to forever: 1% more then the previous year

At 9% APR, what is the present value

infinity

978.24

1027.15

1,078.51

1,132.43

Answer 1

Value of cashflows in year 2 is given by value in year 1 * (1 + growth rate)

value in year 2 = 50*(1+0.04) = 52

Similarly values in each year is given in the table below:

Year	Growth	Value
1		50.0000
2	4%	52.0000
3	4%	54.0800
4	4%	56.2432
5	4%	58.4929
6	4%	60.8326
7	1%	61.4410

From year 7, it grows at constant rate, it becomes a growing perpetuity

The present value of growing perpetuity is obtained as terminal value (TV) in year 6.

Terminal Value (TV) of growing perpetuity is given by, Cn/(r-g)

where Cn is cash flow when growth rate becomes constant (here cash flow in year 7 = 61.441)

r is APR = 9%

g is forever growth rate = 1%

Therefore, TV in year 6 = 61.441/(0.09-0.01)

= 768.0121

Pesent value of cashflows is given by, PV = C/(1+r)^t

where C is cashflow in respective year t

r is APR = 9%

Therefore, PV of all cashflows = Sum(PV of cashflows in year 1 to 6) + PV of TV in year 6

PV for each cashflow using the formula is shown below:

	Year	C	PV calculation	PV
	1	50.0000	C1/(1+r)^1	45.87156
	2	52.0000	C2/(1+r)^2	43.76736
	3	54.0800	C3/(1+r)^3	41.75968
	4	56.2432	C4/(1+r)^4	39.8441
	5	58.4929	C5/(1+r)^5	38.01639
	6	60.8326	C6/(1+r)^6	36.27252
TV==>	6	768.0121	C6/(1+r)^6	457.9405

Hence, PV of all cashflows = Sum of all PV in the table = 703.4722

Since 703.47 is not given in any options, none of the options is correct.

Correct answer is $703.47.