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1. A motor manufacturer is to develop a new car model to be produced from 1 January2002 for six years until 31 December 2007. The development cost will be §33 million,of which §18 million will be incurred on 1 January 2000, §10 million on 1 July 2000and §5 million on 1 January 2001. The production cost of each car is assumed tobe incurred at the beginning of the calendar year of production and will be §9,000during 2002. The sale price of each car is assumed to be received at the end ofthe calendar year of production. Both the production costs and the sale prices areassumed to increase by 5.00% on each 1 January, the first increase occurring on 1January 2003. It is also assumed that 5,000 cars will be produced each year andthat all will be sold. The sale price of each car produced in 2002 is §12,100.(a) Calculate the discounted payback period at an effective rate of interest of 9.00%per annum.(b) Without doing any further calculations, explain whether the discounted payback period would be greater than, equal to, or less than the period calculatedin (a) if the effective rate interest were substantially less than 9.00% per annum

Question

  1. A motor manufacturer is to develop a new car model to be produced from 1 January2002 for six years until 31 December 2007. The development cost will be §33 million,of which §18 million will be incurred on 1 January 2000, §10 million on 1 July 2000and §5 million on 1 January 2001. The production cost of each car is assumed tobe incurred at the beginning of the calendar year of production and will be §9,000during 2002. The sale price of each car is assumed to be received at the end ofthe calendar year of production. Both the production costs and the sale prices areassumed to increase by 5.00% on each 1 January, the first increase occurring on 1January 2003. It is also assumed that 5,000 cars will be produced each year andthat all will be sold. The sale price of each car produced in 2002 is §12,100.(a) Calculate the discounted payback period at an effective rate of interest of 9.00%per annum.(b) Without doing any further calculations, explain whether the discounted payback period would be greater than, equal to, or less than the period calculatedin (a) if the effective rate interest were substantially less than 9.00% per annum
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Solution

The question is asking for two things:

(a) The discounted payback period at an effective interest rate of 9.00% per annum. (b) An explanation of whether the discounted payback period would be greater than, equal to, or less than the period calculated in (a) if the effective interest rate were substantially less than 9.00% per annum.

Let's start with (a):

Step 1: Calculate the total development cost. This is given as $33 million, incurred at different times.

Step 2: Calculate the total production cost for each year. This starts at $9,000 per car in 2002 and increases by 5.00% each year. Multiply this by the number of cars produced each year (5,000) to get the total production cost for each year.

Step 3: Calculate the total sales for each year. This starts at $12,100 per car in 2002 and increases by 5.00% each year. Multiply this by the number of cars sold each year (5,000) to get the total sales for each year.

Step 4: For each year from 2002 to 2007, calculate the net cash flow. This is the total sales minus the total production cost.

Step 5: Discount each year's net cash flow back to the present (1 January 2000) using the effective interest rate of 9.00% per annum.

Step 6: Sum these discounted cash flows and subtract the total development cost to get the net present value (NPV).

Step 7: The discounted payback period is the time it takes for the cumulative discounted cash flows to equal the initial investment. Find the year in which the NPV becomes positive.

For (b), if the effective interest rate were substantially less than 9.00% per annum, the discounted payback period would be less. This is because a lower discount rate increases the present value of future cash flows, meaning the initial investment is recovered more quickly.

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