Question

Turner Video will invest $74,500 in a project. The firm’s cost of capital is 12 percent. The investment will provide the following inflows. Use Appendix A for an approximate answer but calculate your final answer using the formula and financial calculator methods.

Year	Inflow
1	$	23,000
2		25,000
3		29,000
4		33,000
5		37,000

The internal rate of return is 15 percent.

a. If the reinvestment assumption of the net present value method is used, what will be the total value of the inflows after five years? (Assume the inflows come at the end of each year.) (Do not round intermediate calculations and round your answer to 2 decimal places.)
  

   

b. If the reinvestment assumption of the internal rate of return method is used, what will be the total value of the inflows after five years? (Use the given internal rate of return. Do not round intermediate calculations and round your answer to 2 decimal places.)
  

c. Which investment assumption is better?

Answer 1

a) NPV assumes that all cash inflows are reinvested at the cost of capital, i.e., 12%.

Future value of an amount is computed as follows -

FV = Amount x (1 + r)ⁿ where r is the rate of interest at which amount is reinvested and n is the no. of years remaining

Amount invested at the end of year 1 will reinvested for 4 more years till year 5. Similarly, amount invested at the end of year 2, 3, 4 will be reinvested for 3, 2, 1 years respectively. Amount at the end of year 5 will be received as is -

Total value of cash inflows

Year	Future Value of Cash Inflows
1	$23000 x (1 + 0.12)4 = $36,190.95
2	$25000 x (1 + 0.12)3 = $35,123.20
3	$29000 x (1 + 0.12)2 = $36,377.60
4	$33000 x (1 + 0.12)1 = $36,960
5	$37000
Total	$181,651.75

b) IRR method assumes the cash inflows are invested @IRR, i.e., 15% -

Total value of cash inflows

Year	Future Value of Cash Inflows
1	$23000 x (1 + 0.15)4 = $40,227.14
2	$25000 x (1 + 0.15)3 = $38,021.88
3	$29000 x (1 + 0.15)2 = $38,352.50
4	$33000 x (1 + 0.15)1 = $37,950
5	$37000
Total	$191,551.52

c) Investment assumption of NPV is better since IRR can lead to very high and unrealistic expectations as IRRs tend to be very high.