Capital rationing and sensitivity analysis

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Capital rationing

A company has $24 million cash available and could spend this on three of Ansoff matrix quadrants.

Project 1: Market penetration: Cost $8m; inflows $2.4m pa for 10 years

Project 2: Market development: Cost $10m; inflows $3.5m pa for 10 years

Project 3: Diversification: Cost $12m; inflows $3.2m per year for 10 years

The company has decided to use a discount rate of 10% when evaluating their net present value.

Required

(a) Determine which combination of projects would maximise the company’s NPV if the projects are indivisible.

(b) Comment on using 10% for all three evaluations.

Note: the 10 year 10% cumulative discount factor is 6.145

Capital rationing

(a) Project 1 NPV = -$8m + 6.145 x 2.4 = $6.7m

Project 2 NPV = -$10m + 6.145 x 3.5 = $11.5m

Project 3 NPV = -$12m + 6.145 x 3.2 = $7.7m

Possible combinations	NPV
Project 1 + project 2	6.7 + 11.5 = 18.2
Project 1 + project 3	6.7 + 7.7 = 14.4
Project 2 + project 3	11.5 + 7.7 = 19.2

The best combination using the company’s assumptions is to undertake Project 2 + Project 3 which are predicted to result in an NPV of $19.2m

(b) Generally, the different quadrants in Ansoff’s matrix are expected to have different risk return characteristics.

Market penetration means the organisation is on its home ground (same products and markets) so risk should be low.

Market development means that the company is launching into a new, relatively unknown market, so risks are higher.

Diversification is riskiest of all and companies have a very high chance of failure.

Given the three risks characteristics of the different options, it might not be wise to evaluate all NPVs using 10%. For example, it might be appropriate to evaluate Project 3 using a 15% (a 3% risk premium). That would reduce that project’s NPV to:

NPV = -$12m + 5.019^* x $3.2m = 4.1

(* the 10 year 15% cumulative factor)

Project 1 and Project 2 would then show the highest NPV.

(c) If the projects were infinitely divisible, then the approach would be to calculate the NPV per $ needed in the capital restricted period. This gives an ‘earning rate’ per $ invested and money would be allocated to the highest earning rate projects first.

Project 1 NPV/$ = 6.7/8 = 0.84

Project 2 NPV/$ = 11.5/10 = 1.15

Project 3 NPV/4 = 7.7/12 = 0.64

So Project 2 then Project 1 would be done in preference, leaving $6m that would be enough to undertake 50% of Project 3.

NPV = 6.7 + 11.5 + 0.5 x 7.7 = 22.05.

Sensitivity analysis

Here is a project appraised at a discount rate of 10%. Sales volume is estimated at 1,000 units per year.

Time	Flow	$	*10% Discount* *factor*	DCF $
0	Cost	(130,000)	1	(130,000)
1 – 4	Sales	1,000 @$100 = $100,000	3.17	317,000
1 – 4	Marginal costs	1,000 @$60 = ($60,000)	3.17	(190,200)
4	Scrap	25,000	0.683	17,075
			NPV	13,875

The NPV is positive so the conventional advice would be to accept the project. However, the sensitivity of this recommendation to the various assumptions should be examined. This is done by seeing how far an assumption can change before the NPV = 0. Each assumption has to be assessed separately.

Required

(a) Examine the sensitivity of the solution to:

(b) Initial cost

(d) Sales volume

(e) Scrap value

(f) Discount rate

Sensitivity analysis

(a) If the NPV is to be zero, the cost must rise by $13,875.

Sensitivity = 13,875/130,000 = 10.7%

(b) Selling price affects the revenue figure. If its PV of $317,000 falls 13,875 then NPV = 0 .

Sensitivity = 13,875/317,000 = 4.4%

Sensitivity = 13,875/126,800 = 10.9%

(d) The PV of the scrap value must fall by $13,875 to produce a zero NPV.

Sensitivity = 13,875/17,075 = 82%

(e) To work out the sensitivity to the discount rate, the IRR has to be calculated. So, NPV at 20%:

Time	Flow	$	*10% Discount* *factor*	DCF $
0	Cost	(130,000)	1	(130,000)
1 – 4	Sales	1,000 @$100 = $100,000	2.59	259,000
1 – 4	Marginal costs	1,000 @$60 = ($60,000)	2.59	(155,400)
4	Scrap	25,000	0.482	12,050
			NPV	(14,350)

IRR = 10 + (20 – 10) x13,875(13,875 + 14,350) = 14.9, or around 15%

So, the conclusion is very sensitive to the selling price, which only needs to fall by about 4.4% before the project just breaks even. Not only is 4.4% small, but the selling price must be difficult to estimate.

The cost could rise by about 10%. Not a large over-run, but at least cost is easier to predict and control than future flows.

Scrap value could fall by 82% - a large fall, but it will usually be difficult to predict the scrap amount.

The discount rate can rise from 10% to 15% (50%) and that would probably be judged unlikely.