Question

Project Z has a cost of $1.5 million to start up (i.e., at time t=0), and is expected to produce a uniform cash flow stream for 8 years (i.e., the cash flows are expected to be the same in years t=1 through t=8). Project Z’s IRR is 13.5%, while it’s cost of capital is 11.25%. Find project Z’s NPV and its MIRR.

please show all the fraction numbers and be easy to follow

no excel or financial calculator answer please show how u get to the numbers. please dont write any number without the formula and be specific as much as you can

Answer 1

We need to first find out the annual cash flows

IRR is the rate of return that makes initial investment equal to presnet value of cash inflows

Present value = Annuity * [1 - 1 / (1 + IRR)^time] / IRR

1,500,000 = Annuity * [1 - 1 / (1 + 0.135)^8] / 0.135

1,500,000 = Annuity * [1 - 0.363106] / 0.135

1,500,000 = Annuity * 4.717735

Annuity = $317,949.1652

1)

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

NPV = Annuity * [1 - 1 / (1 + rate)^time] / rate - Initial investment

NPV = 317,949.1652 * [1 - 1 / (1 + 0.1125)^8] / 0.1125 - 1,500,000

NPV = 317,949.1652 * [1 - 0.426187] / 0.1125 - 1,500,000

NPV = 317,949.1652 * 5.100563 - 1,500,000

NPV = $121,719.78

2)

Future value of annual cash flows = Annuity * [(1 + rate)^time - 1] / rate

Future value of annual cash flows = 317,949.1652 * [(1 + 0.1125)^8 - 1] / 0.1125

Future value of annual cash flows = 317,949.1652 * [2.34639 - 1] / 0.1125

Future value of annual cash flows = 317,949.1652 * 11.967909

Future value of annual cash flows = 3,805,186.708

MIRR = (Future value / initial investment)^1/time - 1

MIRR = (3,805,186.708 / 1,500,000)^1/8 - 1

MIRR = (2.536791)^1/8 - 1

MIRR = 1.1234 - 1

MIRR = 0.1234 or 12.34%