A cash flow at time zero (now) of $11,454 is equivalent to another cash flow tha

Question

A cash flow at time zero (now) of $11,454 is equivalent to another cash flow that is an EOY annuity of $2,200 over seven years (starting at year 1). Each of these two cash-flow series is equivalent to a third series, which is a uniform gradient series. What is the value of G for this third series over the same seven-year time interval? Assume that the cash flow at the end of year one is zero. Choose the correct answer below OA. $817 O B. $329 O C. $582 OD, $1,200 0 E. Not enough information given.

Explanation / Answer

Finding out implied rate of interest:

Problem implies, an annuity EOY of 2,200 for seven years has a present value of 11,454

at an interest rate of 8% the above statement holds correct.

calculation is as follows:

Gradient cash flow:

this cash flow increases by an amount equal to G every year till the end of the series.

Evaluation of options:

If the present value calculated using the given gradient amount of any of the given options matches the present value of cash flow given above of $11,454 that will be the correct option

Option A. $817

calcuation of present value of cash flows with a G of 817

Note: cash flow for year 1 is 0 as given and from year 2 cash flow increases every year by 817

Option A. is the correct option as it matches the present value approximately ( the difference can be due to rounding off)

Explanation for incorrect options:

Option B. 329

Total present value is not equal to given amount of $11,454

Option C.582

Option D. 1200

Option E. is incorrect as 817 is the correct amount given in option .A

Note:

The present value factors are taken at an interest rate of 8% calculated above.

Present value of annuity= P* [ [1- (1+r)-n ]/r ] P= Periodic payment                            2,200 r= Annual interest 8.00% n= Number of years 7 Present value of annuity= 2200* [ (1- (1+0.08)^-7)/0.08 ] Present value of annuity= 11,454.01

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.