c) A phone manufacturer is to develop a new chip to be produced from 1 January 2008 until 31 December 2020. Development begins on 1 January 2006 The cost of development comprises f9 million payable on 1 January 2006 and f12 million payable continuously during 2007. From 1 January 2008 the chip will be ready for production and it is assumed that income will be received half yearly in arrear at a rate of E5 million per annum. i)Calculate the discounted payback period at an effective rate of interest of 9% per annum. [6 Marks] ii) Without doing any further calculations, explain whether the discounted payback period would be greater than , less than or equal to that given in part (i) if the effective interest rate were substantially greater than 9% per annum. [2 Marks]

Question

c) A phone manufacturer is to develop a new chip to be produced from 1 January 2008 until 31 December 2020. Development begins on 1 January 2006 The cost of development comprises f9 million payable on 1 January 2006 and f12 million payable continuously during 2007. From 1 January 2008 the chip will be ready for production and it is assumed that income will be received half yearly in arrear at a rate of E5 million per annum. i)Calculate the discounted payback period at an effective rate of interest of 9% per annum. [6 Marks] ii) Without doing any further calculations, explain whether the discounted payback period would be greater than , less than or equal to that given in part (i) if the effective interest rate were substantially greater than 9% per annum. [2 Marks]

Answer 1

i) To calculate the discounted payback period, we need to find the time it takes for the present value of the cash inflows to equal the initial investment. The initial investment is the sum of the development cost of £9 million and the continuous cost of £12 million during 2007, which is £21 million.The cash inflows start from 1 January 2008 and are received half-yearly at a rate of £5 million per annum. To find the present value of these cash inflows, we need to discount them using the effective interest rate of 9% per annum.The formula for the present value of an annuity is:PV = C * [(1 - (1 + r)^(-n)) / r]where PV is the present value, C is the cash inflow per period, r is the discount rate, and n is the number of periods.In this case, the cash inflow per period is £5 million, the discount rate is 9% per annum, and the number of periods is 6 (half-yearly for 3 years).Using the formula, we can calculate the present value of the cash inflows:PV = £5 million * [(1 - (1 + 0.09)^(-6)) / 0.09]PV = £5 million * [(1 - (1.09)^(-6)) / 0.09]PV = £5 million * [(1 - 0.5645) / 0.09]PV = £5 million * [0.4355 / 0.09]PV = £5 million * 4.8522PV = £24.261 millionSince the initial investment is £21 million, the discounted payback period is less than 1 year.ii) If the effective interest rate were substantially greater than 9% per annum, the discounted payback period would be less than that given in part (i). This is because a higher discount rate would result in a lower present value of the cash inflows, requiring a shorter payback period to equal the initial investment.

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