Question

Please solve without using excel: need to see work and steps

NPVIRR. Consider projects A and B: Cash Flows (dollars) C1 -30,000 21,000 21,000 -50,000 33,000 33,000 Project Co C2 NPV at 10% +$6,446 +7,273 a. Calculate IRRs for A and B. b. Which project does the IRR rule suggest is best? c. Which project is really best?

Answer 1

a)

IRR is the rate at which NPV is zero. Internal Rate of Return will be calculated by trail and error method.

IRR for Project A

To have an approximate idea about such rate we can calculate the guidance rate to start with.

It represents the same relationship of investment and cash inflows as in case of payback period calculation, therefore it is known as fake payback period,

F = I/C

where,

F = Fake payback period

I = Original Investment

C = Average Cash Inflow per annum

Factor for the project = 30000/21000

= 1.4286 (also known as fake payback period)

The factor will be located from the Present Value Annuity Factor table,

The Approx. value of 1.4286 is located against 25% in 2 years.

Hence, let discount rate is 25%.,

At 25%,

NPV = PV of Cash inflows - PV of Cash Outflows

= 21000*PVAF(2 years, 25%) - 30000

= 21000*1.440 - 30000

= 30240 - 30000

= 240

To make it zero, the present value of cash inflows is to be reduced. Therefore, a higher discount rate,

let discount rate is 30%,

At 30%,

NPV = PV of Cash inflows - PV of Cash Outflows

= 21000*PVAF(2 years, 30%) - 30000

= 21000*1.361 - 30000

= 28581 - 30000

= - 1419

IRR may be calculated by Forward method and backward method,

By Forward Method,

IRR = 25% + NPV at 25 %/Total difference * Difference in rate

= 25 + 240/1659 * 5

= 25 + 0.72

= 25.72%

IRR for Project A is 25.72 %.

IRR for Project B

In the same way as above,

Factor for the project = 50000/33000

= 1.52 (also known as fake payback period)

The factor will be located from the Present Value Annuity Factor table,

The Approx. value of 1.52 is located against 20% in 2 years.

Hence, let discount rate is 20%.,

At 20%,

NPV = PV of Cash inflows - PV of Cash Outflows

= 33000*PVAF(2 years, 20%) - 50000

= 33000*1.528 - 50000

= 50424 - 50000

= 424

To make it zero, the present value of cash inflows is to be reduced. Therefore, a higher discount rate,

let discount rate is 22%,

At 22%,

NPV = PV of Cash inflows - PV of Cash Outflows

= 33000*PVAF(2 years, 22%) - 50000

= 33000*1.492 - 50000

= 49236 - 50000

= - 764

IRR may be calculated by Forward method and backward method,

By Forward Method,

IRR = 20% + NPV at 20 %/Total difference * Difference in rate

= 20 + 424/1188 * 2

= 20 + 0.71

= 20.71%

IRR for Project B is 20.71 %.

b)

The decision for IRR is to invest in a project if its rate of return is greater than its cost of capital.

In this problem, both project have greater IRR than cost of capital (i.e 10%),

Hence both should be accepted, however project having higher IRR should be accepted, because cost of capital is same for both project.

So, Project A is best.

c)

Decision based on NPV is that Project having positive NPV should be accepted.

However, in case of positive NPV in both Project, Project having higher NPV should be accepted.

Hence, Project B is best.