Raiders Ltd is a private limited company financed entirely by ordinary shares. Its effective cost of capital, net of tax, is 10 per cent p.a. The directors are considering the company’s capital investment programme for the next two years, and have reduced their initial list of projects to four. Details of the projects’ cash flows (net of tax) are as follows (in £000):

Project Immediately After 1 year After 2 years After 3 years NPV

(at 10%)

IRR

(to nearest 1%)

A -400 +50 +300 +350 +157.0 26%

B -300 -200 +400 +400 +150.0 25%

C -300 +150 +150 +150 +73.5 23%

D 0 -300 +250 +300 +159.5 50%

None of the projects can be delayed. All projects are divisible; outlays may be reduced by any proportion and net inflows will then be reduced in the same proportion. No project can be undertaken more than once. Raiders Ltd is able to invest surplus funds in a bank deposit account yielding a return of 7 per cent p.a., net of tax.

Required

(a) Prepare calculations showing which projects Raiders Ltd should undertake if capital for immediate investment is limited to £500,000, but is expected to be available without limit at a cost of 10 per cent p.a. thereafter.

(b) Provide a mathematical programming formulation to assist the directors of Raiders Ltd in choosing investment projects if capital available immediately is limited to £500,000, capital available after one year is limited to £300,000, and capital is available thereafter without limit at a cost of 10 per cent p.a.

(c) Outline the limitations of the formulation you have provided in (b).

(d) Comment briefly on the view that in practice capital is rarely limited absolutely, provided that the borrower is willing to pay a sufficiently high price, and that in consequence a technique for selecting investment projects that assumes that capital is limited absolutely is of no use.