Question

Suppose your father decides to invest $10 million in a factory to produce automotive spare part. This factory will enable the firm to produce 8000 parts per month for 20 years at a cost of $42.50 each. The parts could be sold for $52.50 each. Assume that after 20 years, the factory will be absolute but can be sold for scrap for $1 million.

1. If the opportunity cost of funds is 7%, is this a good investment?

2. Suppose the factory will take a year to build: $5 million is spent right away, and another $5 million is spect next year. Also, the factory is supposed to lose $1 million in its first year of operations and $0.5 million in its second year. Afterwards, it will earn $0.96 million a year until year 20, when it will be scraped for $1 million, as before. If the opportunity cost for fund is 4%, should father build this factory.

3. Suppose, you read in the Wall Street Journal an economic report that paints some uncertainities over the future demand and price of the product. How should you take this uncertainties into account to determine if the investment is worthwhile.

Answer 1

(1)

Annual Net profit = Units x (Price - Unit cost) = 8,000 x $(52.5 - 42.5) = 8,000 x $10 = $80,000

Present Worth (PW) ($) = - 10,000,000 + 80,000 x P/A(7%, 20) + 1,000,000 x P/F(7%, 20)

= - 10,000,000 + 80,000 x 10.594** + 1,000,000 x 0.2584** = - 10,000,000 + 847,520 + 258,400

= - 8,894,080

Since PW < 0, this is not a good investment.

(2) In this case,

PW ($Million) = - 5 - 5 x P/F(4%, 1) - 1 x P/F(4%, 1) - 0.5 x P/F(4%, 2) + 0.96 x P/A(4%, 18) x P/F(4%, 2)

= - 5 - 5 x 0.9615** - 1 x 0.9346** - 0.5 x 0.9246** + 0.96 x 12.6593** x 0.9246**

= - 5 - 4.81 - 0.93 - 0.46 + 11.24

= 0.04

Since PW > 0, this factory should be built.

(3)

In order to account for uncertainties of cash flows in future, I should use a higher discount rate (opportunity cost) while computing the present worth, to reflect higher risk.

**From P/A and P/F Factor tables