Q. The management of Comfy Hotels Ltd is attempting to evaluate the feasibility of investing £125,000 in upgrading and extending its bar, kitchen and dining room facilities. The scheme is assumed to have a ten-year life, a scrap or terminal value of nil and is expected to increase annual net profits by £15,000, after charging annual depreciation of £12,500. For a project of this type, management usually prefers a payback period of less than 6 years. Using a cost of capital of 12 per cent, where appropriate, and ignoring taxation, you are required to determine:

(a) Payback period (PPB);

(b) Average accounting rate of return (AARR);

(c) Net present value (NPV);

(d) Internal rate of return (IRR);

(e) The financial acceptability of the project, based upon the above data.

ANSWER:

a) Payback Period (PPB)

Formula:

Initial Investment (cash outlay) on project

PPB = ____________________________________________________

Annual net Cash Inflows from the project.

Initial Investment = £125,000

Annual net cash flow = £ 15,000 + £12,500 = £ 27,500

£ 125,000

PPB = ______________ = 4.5 yrs.

£ 27,500

By using Payback Method Comfort Hotel will undertake the project since the Payback period is 4.5 yrs, that is the actual payback period is less than the predetermined maximum period.

b) Average Accounting Rate of Return (AARR)

Formula:

Average Accounting Profit

AARR = _____________________________________________ x 100

(Initial Outlay + residual value)/2

Average Accounting Profit = £15,000

Initial Outlay = £ 125,000

Residual Value = 0

£ 15,000 15,000

AARR = _______________________ X 100 = ___________ X 100 = 24

( £ 125,000 + 0) / 2 62,500

c) Net Present Value:

Formula:

n

NPV = - Io + ∑ NCF

t = 1 (1+r)n

Whereby

NCF = Net Cash Flow at end of year t = £27,500

Io = Initial Investment / Cash Outlay = £125,000

t = any year

r = required rate of return = 12%

n = project expected life = 10

Year Net Cash Flow (NCF) x Discount Rate (r) = PV

£ 12%

0 (125,000) (125,000)

1 – 10 27,500 5.650 155,375

NPV = 30,375

======

d) Internal Rate of Return (IRR)

Formula:

n

1. 0 = - Io + ∑ NCF

t = 1 (1+IRR)n

NPV1

2. IRR = r1 -------------------- x ( r2 –r1)

NPV1 + NPV2

To determine the internal rate of return we use the trial and error approach

At the discount rate of 12% the NPV is 30,375 positive, at the discount rate of 18% the NPV is – 1,415. This reveal that the IRR lies between 12 – 18 percent.

Therefore

r1 = 0.12 NPV1 = 30,375

r2 = 0.18 NPV2 = - 1,415

30,375 30,375

IRR = 12 + --------------------- x (18 – 12) = 12 +----------- x 6

30,375 + 1,415 31,790

= 12 + (0.95 x 6)

= 17.73% says 18%

A project yields 18 percent, which is greater than the cost of capital or required rate of return of 12%, therefore it is acceptable using IRR criterion

e). - By using Payback Method Comfort Hotel will undertake the project since the

Payback period is 4.5 yrs, that is the actual payback period is less than the

predetermined maximum period.

- Accounting Rate of Return is 24% if the minimum required IRR IS greater than 24 the project is not acceptable but if the minimum required IRR is less than 24% say 12% the project is acceptable.

- Net Present Value (NPV) is 30,375, since the NPV is positive the project is considered acceptable.

- Internal Rate of Return is 18% that is IRR is greater than the required rate of return which is 12% the project is considered acceptable.

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