Question

Margaret has a project with a $29,000 first cost that returns $4000 per year over its 10 -year life. It has a salvage value of $4000 at the end of 10 years. If the MARR is 13 percent, what is the future worth of this project after 10 years?

What is the discounted payback period for this project? Assume the savings are earned at year-end. Click the icon to view the table of compound interest factors for discrete compounding periods when i=13%.

The future worth of the project in 10 years is about $ ___.

(Type an integer or decimal rounded to two decimal places as needed.)

Determine the discounted payback period for the project. Select the correct choice below and, if necessary, fill in the answer box to complete your choice.

A. The discounted payback period for the project is year(s), which is less than the life of the project. (Round up to the nearest whole number.)

B. The discounted payback period for the project is greater than the life of the project.

Answer 1

Part 1

Future value = FV of first cost+ FV of annuity + salvage value

= PV*(1+r)^n+ A*((1+r)^n-1)/r+ Salvage value

= 29000*(1+13%)^10+ 4000*((1+13%)^10-1)/13%+ 4000

=29000*3.39456739+ 4000*18.41974915+ 4000

=98,442.45+73,679.00+4000

=176,121.45

Part 2: B the discounted payback period is more than the life of the project.

The Discounted cash flow table is as follows

Year	Cash flows	Discounted cash flow	Curmulative DCF
0	-29000	-29,000.00	-29,000.00
1	4000	3,539.82	-25,460.18
2	4000	3,132.59	-22,327.59
3	4000	2,772.20	-19,555.39
4	4000	2,453.27	-17,102.11
5	4000	2,171.04	-14,931.07
6	4000	1,921.27	-13,009.80
7	4000	1,700.24	-11,309.56
8	4000	1,504.64	-9,804.92
9	4000	1,331.54	-8,473.38
10	8000	2,356.71	-6,116.67

 

Since the cumulative DCF is still negative, the discounted payback is more than the life of the project. The initial cost is never recovered.

 

Working

Future value is 176,121.45.