Consider the following timeline: If the current market rate of interest is 12%, then the value of the cash flows in year 0 and year 2 as of year 1 is closest to:
A)$257.29
B)-$78.71
C)$1.29
D)$78.71

Question

Consider the following timeline:  If the current market rate of interest is 12%, then the value of the cash flows in year 0 and year 2 as of year 1 is closest to:
A)$257.29 
B)-$78.71 
C)$1.29 
D)$78.71

Quizplus · Accepted Answer

The given timeline can be interpreted as follows: 
- There is a cash flow of $100 in year 0 
- There is a cash flow of $200 in year 2

To find the value of these cash flows in year 1, we need to discount them by the market rate of interest of 12%.

For the cash flow of $100 in year 0: 
Discounted value = $100/1.12^1 = $89.29

For the cash flow of $200 in year 2: 
Discounted value = $200/1.12^2 = $163.43

Adding these two discounted values, we get: 
$89.29 + $163.43 = $252.72

However, we need to express this value as of year 1. To do so, we need to compound the value back by one year: 
Value as of year 1 = $252.72(1.12^1) = $283.12

The closest answer choice to this value is B) -$78.71. Note that the question asks for the values to be expressed with a sign, indicating whether they are positive or negative. A negative value means that the investor would need to pay that amount to receive the cash flows, which makes sense given that the market rate is higher than the value of the cash flows.

Consider the Following Timeline: If the Current Market Rate