Additional Problems with Answers Problem 1

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Additional Problems with AnswersProblem 1

Computing Payback Period and Discounted Payback Period.

Regions Bank is debating between two the purchase of two software

systems; the initial costs and annual savings of which are listed

below. Most of the directors are convinced that given the short

lifespan of software technology, the best way to decide between the

two options is on the basis of a payback period of 2 years or less.

Compute the payback period of each option and state which one

should be purchased.

One of the directors states, “I object! Given our hurdle rate of 10%,

we should be using a discounted payback period of 2 years or less.”

Accordingly, evaluate the projects on the basis of the DPP and state

your decision.


Additional Problems with AnswersProblem 1 (Answer)

Software Option A PVCF@10%

Software Option B PVCF@10%

($1,875,000) $ (1,875,000.00) ($2,000,000) $ (2,000,000.00) $1,050,000 $ 954,545.45 1,250,000 $ 1,136,363.64 $900,000 $ 743,801.65 $800,000 $ 661,157.02 $450,000 $ 338,091.66 $600,000 $ 450,788.88

Payback period of Option A = 1 year + (1,875,000-1,050,000)/900,000 = 1.92 yearsPayback period of Option B = 1year + (2,000,000-1,250,000)/800,000 = 1.9375 years.Based on the Payback Period, Option A should be chosen.


Additional Problems with AnswersProblem 1 (Answer) (continued)

For the discounted payback period, we first discount the cash flows at 10% for the respective number of years and then add them up to see when we recover the investment.

DPP A = -1,875,000 + 954,545.45+743,801.65=-176652.9 still to be recovered in Year 3 DPP A = 2 + (176652.9/338091.66) = 2.52 yearsDPP B = -2,000,000+1, 136,363.64+661157.02 = -202479.34 still to be recovered in Year 3 DPPB = 2 + (202479.34/450788.88) = 2.45 years.

Based on the Discounted Payback Period and a 2 year cutoff, neither option is acceptable.



Computing Net Present Value – Independent projects:

Locey Hardware Products is expanding its product line and its production capacity. The costs and expected cash flows of the two projects are given below. The firm typically uses a discount rate of 15.4 percent.

a. What are the NPVs of the two projects?

b. Which of the two projects should be accepted (if any) and why?


NPV @15.4% = $86,572.61 $20,736.91

Decision: Both NPVs are positive, and the projects are independent, so assuming that Locey Hardware has the required capital, both projects are acceptable.

Year Product Line Expansion

Production Capacity Expansion

0 $ (2,450,000) $ (8,137,250) 1 $ 500,000 $ 1,250,000 2 $ 825,000 $ 2,700,000 3 $ 850,000 $ 2,500,000 4 $ 875,000 $ 3,250,000 5 $ 895,000 $ 3,250,000



KLS Excavating needs a new crane. It has received two proposals from suppliers.

Proposal A costs $ 900,000 and generates cost savings of $325,000 per year for 3 years, followed by savings of $200,000 for an additional 2 years.

Proposal B costs $1,500,000 and generates cost savings of $400,000 for 5 years.

If KLS has a discount rate of 12%, and prefers using the IRR criterion to make investment decisions, which proposal should it accept?



Year

Crane A

Crane B

0 $ (900,000) $ (1,500,000)

1 $ 325,000 $ 400,000

2 $ 325,000 $ 400,000

3 $ 325,000 $ 400,000

4 $ 200,000 $ 400,000

5 $ 200,000 $ 400,000

Required rate of return 12%

IRR 17.85% 10.42%

Decision Accept Crane A IRR>12%



Using MIRR.

The New Performance Studio is looking to put on a new opera.

They figure that the set-up and publicity will cost $400,000.

The show will go on for 3 years and bring in after-tax net cash flows of $200,000 in Year 1; $350,000 in Year 2; -$50,000 in Year 3.

If the firm has a required rate of return of 9% on its investments, evaluate whether the show should go on using the MIRR approach.



The forecasted after-tax net cash flows are as follows: Year After-tax cash flow 0 -$400,000 1 200,000 2 350,000 3 -$50,000

The formula for MIRR is as follows:

Where :

FV = Compounded value of cash inflows at end of project’s life (Year 3)using realistic reinvestment rate (9%);

PV = Discounted value of all cash outflows at Year 0;

N = number of years until the end of the project’s life= 3.



FV3 = $200,000*(1.09)2 + $350,000*(1.09)1

= $237,620 + $381,500 = $619,120

PV0 = $400,000 + $50,000/(1.09)3

=$438,609.17

MIRR = (619,120/$438,609.17)1/3 – 1

= (1.411552)1/3 -1 = 12.18%

The show must go on, since the MIRR = 12.18% > Hurdle rate = 9%



Using multiple methods with mutually exclusive projects: The Upstart Corporation is looking to invest one of 2 mutually

exclusive projects, the cash flows for which are listed below. Their director is really not sure about the hurdle rate that he should use when evaluating them and wants you to look at the projects’ NPV profiles to better assess the situation and make the right decision.

Year A B 0 -454,000 ($582,000) 1 $130,000 $143,333 2 $126,000 $168,000 3 $125,000 $164,000 4 $120,000 $172,000 5 $120,000 $122,000



To get some idea of the range of discount rates we should include in the NPV profile, it is a good idea to first compute each project’s IRR and the crossover rate, i.e. , the IRR of the cash flows of Project B-A as shown below:

Year A B B-A 0 (454,000) ($582,000) ($128,000) 1 $130,000 $143,333 $13,333 2 $126,000 $168,000 $42,000 3 $125,000 $164,000 $39,000 4 $120,000 $172,000 $52,000 5 $120,000 $122,000 $2,000

IRR 0.116 0.102 0.052



So, it’s clear that the NPV profiles will cross-over at a discount rate of 5.2%.

Project A has a higher IRR than Project B, so at discount rates higher than 5.2%, it would be the better investment, and vice-versa (higher NPV and IRR), but if the firm can raise funds at a rate lower than 5.2%, then Project B will be better, since its NPV would be higher.

To check this let’s compute the NPVs of the 2 projects at 0%, 3%, 5.24%, 8%, 10.2%, and 11.6%...



Rate NPV(A) NPV(B) 0.00% 167,000 187,333 3.00% 115,505 123,656 5.24% 81,353 81,353 8.00% 43,498 34,393 10.2% 15,810 0 11.6% 0 -19,658

Note that the two projects have equal NPVs at the cross-over rate of 5.24%. At rates below 5.24%, Project B’s NPVs are higher; whereas at rates higher than 5.24%, Project A has the higher NPV.

Additional Problems with Answers Problem 1

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