Problem:

CM Ltd has been presented with the following project:

A new machine for £250,000 is required at the beginning of the first year. The machine will last for 4 years and thereafter can be disposed of for £25,000. The company's policy is to depreciate this type of machine over its economic life on a straight-line basis.

The demand for the product CF depends on the states of the economy in the future. In the good state, CM Ltd expects to sell 15,000 units per year for the next 4 years. If the economy is bad, sales will fall to 5,000 units per year. Each state of the economy has an equal probability to materialize. Each unit of product CF will be priced at £40. Total variable costs per unit are expected to be £30 for the first year and rise by 10% per year thereafter. The cost of capital (after tax) is 10%. For the purposes of tax, the machine is available for capital allowance relief at 25% per annum on the written down value at the beginning of each year. Any unrelieved capital allowance will be given at the end of the project's life.

Corporate tax at 30% of the taxable profit after capital allowances is payable in the same year as the profit to which the tax is related. The net cash flows (before tax) for the project are assumed to be the taxable profit before capital allowances. All cash flows are assumed to arise at the end of the year except the purchase of the new machine.

Required

i. Calculate the Net Present Value of the project.

ii. By how much does the cost of capital need to change before the NPV of the project becomes zero

Additional Information:

This question is from Finance as well as it is about computation of NPV for a project where a new machine is to be bought by the company as well as use it for 4 years. Depending on the demand for the product, the sales have been estimated. The change in cost of capital before the NPV reaches zero also requires to be computed.