1 A property developer has bought some land for 25,000,000 on which a block of apartments will be built. These apartments will be built over a period of five years starting immediately. Each apartment will take one month to build and will cost 160,000 to build. It is assumed that these building costs will be incurred at the beginning of each month. The number of apartments built each month are given in the spreadsheet CMIB Q1. It is further assumed that the apartments will each be sold for 250,000 three months after they have been built so that e.g. the first apartments are sold after four months. The developer assumes a risk discount rate of 10% per annum effective. (i) Calculate (a) the present value of the land and building costs of the project (b) the present value of the sale proceeds [12] Calculate (a) the accumulated value of the project at the time that the final apartments are sold. (b) the discounted payback period of the project (c) the internal rate of return for the project. [12] It is now assumed that the developer will fund the project by borrowing from a bank at an interest rate of 12% per annum effective. The developer can repay the borrowing at any time from the income from the sale of the apartments and can invest any surplus income in a bank account paying 6% per annum effective. (iii) Calculate the revised accumulated value of the project at the time that the final apartments are sold. [6] The developer is concerned that the original assumptions are too optimistic and now wishes to consider the effects of changing the following assumptions: the building costs are 160,000 for each apartment in the first month but then increase monthly in line with an assumed inflation rate of 3% per annum effective a delay in selling the apartments such that 60% of the apartments are sold three months after they have been built with the other 40% being sold nine months after being built. . (iv) Recalculate the answers to part (ii) assuming a risk discount rate of 10% per annum effective assuming both of the above changes to the assumptions are made. [14] Total 141 1 A property developer has bought some land for 25,000,000 on which a block of apartments will be built. These apartments will be built over a period of five years starting immediately. Each apartment will take one month to build and will cost 160,000 to build. It is assumed that these building costs will be incurred at the beginning of each month. The number of apartments built each month are given in the spreadsheet CMIB Q1. It is further assumed that the apartments will each be sold for 250,000 three months after they have been built so that e.g. the first apartments are sold after four months. The developer assumes a risk discount rate of 10% per annum effective. (i) Calculate (a) the present value of the land and building costs of the project (b) the present value of the sale proceeds [12] Calculate (a) the accumulated value of the project at the time that the final apartments are sold. (b) the discounted payback period of the project (c) the internal rate of return for the project. [12] It is now assumed that the developer will fund the project by borrowing from a bank at an interest rate of 12% per annum effective. The developer can repay the borrowing at any time from the income from the sale of the apartments and can invest any surplus income in a bank account paying 6% per annum effective. (iii) Calculate the revised accumulated value of the project at the time that the final apartments are sold. [6] The developer is concerned that the original assumptions are too optimistic and now wishes to consider the effects of changing the following assumptions: the building costs are 160,000 for each apartment in the first month but then increase monthly in line with an assumed inflation rate of 3% per annum effective a delay in selling the apartments such that 60% of the apartments are sold three months after they have been built with the other 40% being sold nine months after being built. . (iv) Recalculate the answers to part (ii) assuming a risk discount rate of 10% per annum effective assuming both of the above changes to the assumptions are made. [14] Total 141