Question

Consider a one-year project that costs $126,000, provides an income of $70,000 a year for 5 years, and costs $225,000 to dispose of at the very end of the fifth year. Assume that the first payment comes at the start of the year after the project is undertaken. Should the project be undertaken at a 0% discount rate? How about 2%? 5%? 10%? (HINT: To answers these questions use the present discounted value)

Answer 1

Present Value (PV) of cash flows are as follows.

(i) Discount rate = 0%

`\mathrm{PV}(\mathrm{S})=-126,000+70,000 \mathrm{x} \mathrm{P} / \mathrm{A}(0 \%, 5)-225,000 \mathrm{x} \mathrm{P} / \mathrm{F}(0 \%, 5)`
`=-126,000+70,000 * 5-225,000`

= - 1

Since PV < 0, the project should not be undertaken.

(ii) Discount rate = 2%

`\mathrm{PV}(\mathrm{S})=-126,000+70,000 \mathrm{x} \mathrm{P} / \mathrm{A}(2 \%, 5)-225,000 \mathrm{x} \mathrm{P} / \mathrm{F}(2 \%, 5)`

`|=-126,000+70,000 * 4.7135-225,000 * 0.9057`

= 156

Since PV > 0, the project should be undertaken.

(iii) Discount rate = 5%

`\mathrm{PV}(\mathrm{S})=-126,000+70,000 \mathrm{x} \mathrm{P} / \mathrm{A}(5 \%, 5)-225,000 \mathrm{x} \mathrm{P} / \mathrm{F}(5 \%, 5)`

`=-126,000+70,000 * 4.3295-225,000 * 0.7835`

= 772

Since PV > 0, the project should be undertaken.

(ii) Discount rate = 10%

`\mathrm{PV}(\mathrm{S})=-126,000+70,000 \mathrm{x} \mathrm{P} / \mathrm{A}(10 \%, 5)-225,000 \mathrm{x} \mathrm{P} / \mathrm{F}(10 \%, 5)`

`=-126,000+70,000 * 3.7908-225,000 * 0.6209=-126,000+265,356-139,707`

= - 351

Since PV < 0, the project should not be undertaken.