4. On 1 January 2012 an investor has a choice of two projects A and B . Project A involves an initial outlay of ￡100,000 and provides income anmually in arrears of ￡5,000 at the end of the first year, growing at 7% pa, the last payment being on 31 December 2019. The investor will be able to sell the ongoing rights to the project on 31 December 2019 after the payment then due for ￡130,662. Project B also involves an initial cost of ￡100,000 and provides no income , but the investor will be able to sell the rights to the project on 31 December 2019 for pounds 197.750. (a) Calculate the internal rates of return for each project as of 1 January 2012. (b) The investor has no capital for investing in either project, but can borrow ￡100,000 from a bank at 7% pa interest payable annually in arrears. The loan would be repayable on 31 December 2019 at par with no early repayment option. If further loans are required they will also be granted at 7% pa repayable at par on 31 December 2019 with no early repayment option. 6 marks] However, interest on further loans is rolled up to 31 December 2019 . If the investor has any surplus proceeds after paying interest on the original loan as it becomes due, these can be invested at an interest rate of 4% pa effective up to 31 December 2019. Calculate the accumulated profit on each project at 31 December 2019. [14 marks]

(a) To calculate the internal rate of return (IRR) for each project, we need to find the discount rate that makes the net present value (NPV) of the cash flows equal to zero.<br /><br />For Project A:<br />The cash flows are as follows:<br />- Initial outlay: -$100,000<br />- Income in the first year: $5,000<br />- Income in the second year: $5,000 * (1 + 0.07) = $5,350<br />- Income in the third year: $5,000 * (1 + 0.07)^2 = $5,735.50<br />- Income in the fourth year: $5,000 * (1 + 0.07)^3 = $6,147.45<br />- Income in the fifth year: $5,000 * (1 + 0.07)^4 = $6,598.56<br />- Sale price on 31 December 2019: $130,662<br /><br />The NPV equation for Project A is:<br />NPV = -$100,000 + $5,000 / (1 + IRR) + $5,350 / (1 + IRR)^2 + $5,735.50 / (1 + IRR)^3 + $6,147.45 / (1 + IRR)^4 + $6,598.56 / (1 + IRR)^5 + $130,662 / (1 + IRR)^5 = 0<br /><br />For Project B:<br />The cash flows are as follows:<br />- Initial outlay: -$100,000<br />- Sale price on 31 December 2019: $197,750<br /><br />The NPV equation for Project B is:<br />NPV = -$100,000 + $197,750 / (1 + IRR)^4 = 0<br /><br />By solving the NPV equations for both projects, we can find the IRR for each project.<br /><br />(b) To calculate the accumulated profit on each project at 31 December 2019, we need to consider the interest on the original loan and the potential for further loans.<br /><br />For Project A:<br />- The investor borrows $100,000 at 7% pa interest payable annually in arrears.<br />- The loan would be repayable on 31 December 2019 at par with no early repayment option.<br />- Interest on the loan would be $100,000 * 0.07 = $7,000 per year.<br />- The investor would receive the following income from the project:<br /> - Year 1: $5,000<br /> - Year 2: $5,350<br /> - Year 3: $5,735.50<br /> - Year 4: $6,147.45<br /> - Year 5: $6,598.56<br />- The investor would sell the ongoing rights to the project on 31 December 2019 for $130,662.<br />- The accumulated profit would be the sum of the income minus the loan interest and the sale price of the rights.<br /><br />For Project B:<br />- The investor borrows $100,000% pa interest payable annually in arrears.<br />- The loan would be repayable on 31 December 2019 at par with no early repayment option.<br />- Interest on the loan would be $100,000 * 0.07 = $7,000 per year.<br />- The investor would receive no income from the project, but would sell the rights to the project on 31 December 2019 for $197,750.<br />- The accumulated profit would be the sale price of the rights minus the loan interest.<br /><br />By calculating the accumulated profit for each project, we can determine which project would result in a higher profit for the investor at 31 December 2019.