a) NPV Computation:

NPV can be computed by discounting the real cash flows with the company’s real rate of return. Discounting the project real cash flows with the real rate of return produces an NPV of GHS152,666:

End of Year	NCF	Discount Factor @ 8.7%	PV
0	(150,000)	1	(150,000)
1	5,000	0.92	4,600
2	10,500	0.846	8,883
3	25,000	0.779	19,475
4	28,000	0.716	20,048
5	30,000	0.659	19,770
6 and every year thereafter	30,000	7.575	227,250

NPV = 150,026

Comment: Since the NPV of the project is positive, the value of the firm will increase when the project is implemented. The project should therefore be accepted for implementation.

Workings:

1.) Discount rate:

The real rate of return is estimated using the Fisher’s equation as under:

(1+i)=(1+r)(1+h)

Nominal rate, i = 25%
Inflation rate, h = 15%
Therefore, the real rate of return is 8.7%

2.) Discount factor for equal cash flows occurring every year from year 6 to infinity

The equal annual cash flow of GHS30,000 from year 6 to infinity is first discounted as a perpetuity to obtain the terminal value at end of year 5:

Terminal value of constant CF from 6 to infinity =

The terminal value is then discounted as a single amount to obtain the PV at time zero:

PV of constant CF from 6 to infinity =

The aggregate discount factor is therefore 7.575:

Aggregate discount factor =

b) Sensitivity Analysis:

The sensitivity of the project’s NPV to the discount rate can be estimated as the percentage change in the discount rate needed to reduce NPV to zero.

Sensitivity percentage =

Sensitivity percentage =

That is, the discount rate will have to increase by 72.4% for the NPV to reduce to zero. The high percentage increase required in the discount rate for the NPV to drop to zero implies Project PA205 is less sensitive to variation in the discount rate.

IRR Calculation:

The IRR is calculated by trial and error as under:

Setting iL = 15% and iH = 17%, NPVL and NPVH are computed as under:

End of Year	NCF	DF (15%)	PV @15%	DF (17%)	PV @17%
0	(150,000)	1.000	(150,000)	1.000	(150,000)
1	5,000	0.870	4,350	0.855	4,275
2	10,500	0.756	7,938	0.731	7,676
3	25,000	0.658	16,450	0.624	15,600
4	28,000	0.572	16,016	0.534	14,952
5	30,000	0.497	14,910	0.456	13,680
6 and every year thereafter	30,000	6.667 x 0.497	99,405	5.882 x 0.456	80,466

NPV @ 15% = 9,069
NPV @ 17% = (13,351)

The IRR of the project is 15.8%:

c) Project Selection Under Single Period Capital Rationing

i) If projects are independent and divisible

When a firm faces capital rationing for a single period and projects are independent and divisible, funds may be allocated to projects based on the profitability index rankings.

Project	Investment	NPV	PI = NPV/Investment	Rank
PA201	50,000	85,200	1.70	1
PA202	75,000	98,500	1.31	3
PA203	48,000	65,950	1.37	2
PA204	85,000	95,400	1.12	4
PA205	150,000	150,026	1.00	5

Fund Allocation:

Fund allocation to projects based on PI rankings and respective NPV follow:

Project	Investment Required	Fund Allocation	NPV
PA201	50,000	50,000	85,200
PA203	48,000	48,000	65,950
PA202	75,000	75,000	98,500
PA204 (balance)	85,000	27,000	30,299*
PA205	150,000	–	–
		200,000	279,949

That is, the company should invest fully in projects PA201, PA203, and PA202; 31.76% in PA204 (27,000/85,000); and nothing in PA205 which is at the bottom of the ranking. The optimum aggregate NPV is GHS279,949.

Workings:

• NPV from PA204 is its NPV multiplied by the proportion of the investment requirement the company will allocate funds to (i.e. GHS95,400 x 31.76%).

ii) If projects are independent and indivisible

Here we consider a combination of the projects and select the combination that will produce the highest combined NPV. Any unused funds may be invested externally (e.g., in securities).

Combination of Projects	Combined Investment Requirement	Unused Funds	Combined NPV
PA201, PA202, and PA203	173,000	27,000	249,650
PA201, PA203, and PA204	183,000	17,000	246,550
PA201 and PA205	200,000	0	235,226
PA203 and PA205	198,000	2,000	215,976

The company should invest in projects PA201, PA202, and PA203 to earn the highest combined NPV of GHS249,650. The unused funds of GHS27,000 should be invested externally.

d) Practical Ways to Address Capital Constraints:

Practical ways of dealing with capital constraints so as not to lose opportunities to further increase the value of the company include the following:

• Seek joint venture partners to share the project’s investment requirement.
• Use licensing or franchising arrangements to produce and sell the product, earning royalties while avoiding financing of the investment requirements.
• Contract out parts of the project to subcontractors who would finance the project in advance.
• Seek alternative financing such as venture capital and asset securitization.
• Seek grants or aid from the government or organizations if the project aligns with their objectives.