Question

Bill moved in with his mother a few years back. She is now thinking that this was a bad idea so she has promised to give him $10,000 when he leaves the house forever toward the downpayment on a new home. Bill had planned to leave in five year time. However, the offer from his mother has him thinking that he could leave one year earlier than he had planned. As a result, the present value of this offer will:

• be greater than $10,000.

• remain constant.

• decrease.

• increase.

• equal $10,000.

Answer 1

Answer ) Option d) Increase

Solution

Mother promises to give Bill 10,000 USD whenever he leave the house.

Bill's Original Plan to Leave = 5 years

Bill's Revised Plan to leave = 4 years

The present value is the discounted value of the expected income stream over a period of time.

Hence, the present value of the offer will be the discounted value of 10,000 i.e. less than 10,000 USD and will increase over time to become 10,000.

Option a) cannot be the answer since present value can never be greater than the value in future as it is the discounted value.

Option b) is incorrect since present value changes with time and cannot remain constant.

Option c) is incorrect as we will move ahead with time, the present value will increase and cannot decrease further.

Option e) is incorrectsince PV = FV only when the time to maturity becomes nil.