A private corporation is considering a proposed investment in a freeway development. Two alternatives are presented for construction, each offering a return of $2.5m at the end of the first year, rising (compounding) by 8% pa thereafter. The first alternative A provides the full freeway completed at the end of year 1, with a 30 year lifetime. The second alternative B provides a phased investment. An upgrade at year 15 is involved, with a 30 year lifetime. The basic costs and benefits to the Company from each alternative are tabulated below:
(a) Assuming a zero inflation rate, and a discount rate of 8%, derive:
(i) Cash flow diagram for each case, that shows clearly the transactions in the investments over a common period of 30 years.
(ii) Net present value (NPV) for each alternative, as seen by the corporation.
(b) If the discount rate were increased, which of the alternatives would tend to be favoured by the change in rate? (Do not bother to calculate new quantitative NPV results.)
Asm) BSm) Cost or benefit Time Year 40 25 Construction Year 15 65 Operation and Years 1-15 0.5 0.75 Years 16 on 0.75 1 Maintenance Revenue Year 1 (rising at 8% pa 25 25