Question

A firm is evaluating two projects for this year’s capital budget. Its WACC is 14%. Project A costs $6,000 and its expected cash inflows would be $2,000 per year for 5 years. Project B costs $18,000 and its expected cash inflows would be $5,600 per year for 5 years. Calculate NPV and IRR for each project.

Refer to problem 7. Calculate the MIRR and payback for each project.

Refer to Problem 7. Calculate the discounted payback for each project.

Refer to Problem 7. If the projects were mutually exclusive, which one would you recommend? If the projects were independent, which one(s) would you recommend? Explain.

Answer 1

PROJECT A:

NPV = Present value of cash inflows - present value of cash outflows

NPV = -6000 + 2000 / ( 1 + 0.14)¹ + 2000 / ( 1 + 0.14)² + 2000 / ( 1 + 0.14)³ + 2000 / ( 1 + 0.14)⁴ + 2000 / ( 1 + 0.14)⁵  

NPV = -6000 + 1754.386 + 1538.935 + 1349.943 + 1184.161 + 1038.737

NPV = $866.162

IRR is the rate of return that makes NPV equal to 0

NPV = -6000 + 2000 / ( 1 + R)¹ + 2000 / ( 1 + R)² + 2000 / ( 1 + R)³ + 2000 / ( 1 + R)⁴ + 2000 / ( 1 + R)⁵

Using trial and error method, i.e, after trying various values for R, let try R as 19.86

NPV = -6000 + 2000 / ( 1 + 0.1986)¹ + 2000 / ( 1 + 0.1986)² + 2000 / ( 1 + 0.1986)³ + 2000 / ( 1 + 0.1986)⁴ + 2000 / ( 1 + 0.1986)⁵

NPV = 0

Therefore IRR is 19.86%

Future value of year 1 cash flow = 2000 ( 1 + 0.14)⁴ = 3,377.92

Future value of year 2 cash flow = 2000 ( 1 + 0.14)³ = 2,963.088

Future value of year 3 cash flow = 2000 ( 1 + 0.14)² = 2,599.2

Future value of year 4 cash flow = 2000 ( 1 + 0.14)¹ = 2,280

Future value of year 5 cash flow = 2000 ( 1 + 0.14)⁰ = 2000

Total future value = 2000 + 2,280 + 2,599.2 + 2,963.088 + 3,377.92 = 13,220.208

MIRR = ( ?13,220.208 / 6000)^1/5 - 1

MIRR = 1.1712 - 1

MIRR = 0.1712 or 17.12%

Payback period = 6000 / 2000

Payback period = 3 years

Cumulative cash flow for year 0 = -6000

Cumulative cash flow for year 1 = -6000 +  1754.386 = -4,245.614

Cumulative cash flow for year 2 = -4,245.614 + 1538.935 = -2,706.679

Cumulative cash flow for year 3 = -2,706.679 + 1349.943 = -1,356.736

Cumulative cash flow for year 4 = -1,356.736 + 1184.161 = -172.575

Cumulative cash flow for year 5 = -172.575 + 1038.737 = 866.162

172.575 / 1038.737 = 0.166

Discounted payback period = 4 + 0.166 = 4.166 years

PROJECT B:

NPV = Present value of cash inflows - present value of cash outflows

NPV = -18000 + 5600 / ( 1 + 0.14)¹ + 5600 / ( 1 + 0.14)² + 5600 / ( 1 + 0.14)³ + 5600 / ( 1 + 0.14)⁴ + 5600 / ( 1 + 0.14)⁵  

NPV = -6000 + 4912.281 + 4309.018 + 3779.84 + 3315.65 + 2908.465

NPV = $1225.254

IRR is the rate of return that makes NPV equal to 0

NPV = -18000 + 5600 / ( 1 + R)¹ + 5600 / ( 1 + R)² + 5600 / ( 1 + R)³ + 5600 / ( 1 + R)⁴ + 5600 / ( 1 + R)⁵

Using trial and error method, i.e, after trying various values for R, let try R as 16.8

NPV = -18000 + 5600 / ( 1 + 0.168)¹ + 5600 / ( 1 + 0.168)² + 5600 / ( 1 + 0.168)³ + 5600 / ( 1 + 0.168)⁴ + 5600 / ( 1 + 0.168)⁵

NPV = 0

Therefore IRR is 16.8%

Future value of year 1 cash flow = 5600 ( 1 + 0.14)⁴ = 9,458.177

Future value of year 2 cash flow = 5600 ( 1 + 0.14)³ = 8,296.646

Future value of year 3 cash flow = 5600 ( 1 + 0.14)² = 7,277.76

Future value of year 4 cash flow = 5600 ( 1 + 0.14)¹ = 6,384

Future value of year 5 cash flow = 5600 ( 1 + 0.14)⁰ = 5600

Total future value = 5600 + 6,384 + 7,277.76 + 8,296.646 + 9,458.177 = 37,016.583

MIRR = ( ?37,016.583 / 18000)^1/5 - 1

MIRR = 1.1551 - 1

MIRR = 0.1551 or 15.51%

Payback period = 18000 / 5600

Payback period = 3.21 years

Cumulative cash flow for year 0 = -18000

Cumulative cash flow for year 1 = -18000 +  4912.281 = -13,087.719

Cumulative cash flow for year 2 = -13,087.719 + 4309.018 = -8,778.539

Cumulative cash flow for year 3 = -8,778.539 + 3779.84 = -4,998.699

Cumulative cash flow for year 4 = -4,998.699 + 3315.65 = -1,683.049

Cumulative cash flow for year 5 = -1,683.049 + 2908.465 = 1,225.416

1,683.049 / 2908.465 = 0.579

Discounted payback period = 4 + 0.579 = 4.579 years

If the projects were mutually exclusive, we always go by the NPV rule. Project B has a higher NPV, therefore project B should be accepted.

If the projects were independent, both projects should be accepted as both projects has positive NPV, IRR and MIRR greater tha cost of capital.