"Exercise 16-3 Determining the present value of a lump-sum future cash receipt
Marsha Bittner expects to receive a $600,000 cash benefit when she retires five years from today. Ms. Bittner’s employer has offered an early retirement incentive by agreeing to pay her $360,000 today if she agrees to retire immediately. Ms. Bittner desires to earn a rate of return of 12 percent.
Required
a. Assuming that the retirement benefit is the only consideration in making the retirement deci- sion, should Ms. Bittner accept her employer’s offer?
b. Identify the factors that cause the present value of the retirement benefit to be less than $600,000."
(ACC 201 594)
ACC 201. McGraw-Hill Create. <vbk:9781121253193#page(594)>.
To determine whether or not Ms. Bittner should accept her employer's offer, we need to calculate the present value of the cash benefit she will receive after retiring five years from today. The present value is the current value of a future cash flow, taking into account the time value of money.
To calculate the present value, we can use the formula for present value of a lump sum:
PV = FV / (1 + r)^n
Where:
PV = Present value
FV = Future value
r = Rate of return
n = Number of periods
In this case, the future value (FV) is $600,000, the rate of return (r) is 12%, and the number of periods (n) is 5 years. Plugging these values into the formula, we get:
PV = $600,000 / (1 + 0.12)^5
Calculating this, we find that the present value of the retirement benefit is approximately $335,880.
Now, let's move on to part b - identifying the factors that cause the present value of the retirement benefit to be less than $600,000.
The present value of a future cash flow is affected by several factors such as the time value of money, the rate of return, and the time period involved. In this case, the main factor causing the present value to be less than $600,000 is the rate of return.
When we calculate the present value, we discount the future cash flow by the rate of return. In this case, Ms. Bittner desires to earn a rate of return of 12 percent, which is higher than 0%. This means that the higher the rate of return, the lower the present value of the future cash flow will be.
Therefore, the combination of time value of money and Ms. Bittner's desired rate of return causes the present value of the retirement benefit of $600,000 to be reduced to $335,880.