# Complex question on NPV help please

• This topic has 1 reply, 1 voice, and was last updated 2 months, 3 weeks ago by Guest.
Viewing 2 posts - 1 through 2 (of 2 total)
• Author
Posts
• #3063330

I'm trying to to understand the fundamental concept of this question. I understand the concept of NPV and and how annuity calculation comes into play of calculating NPV but I cannot wrap my head around UNDERSTANDING this question as a whole, even after looking at the solution.

Para Co. is reviewing the following data relating to an energy saving investment proposal:

Cost \$50,000
Residual at the end of 5 years \$10,000
Present ‘value of an annuity of 1 at 12% for 5 years 3.60
Present ‘.value of 1 due in 5 years at 12% 0.57

What would be the annual sayings needed to make the investment realize a 12% yield?

a, \$8,189
b, \$12,306
c, \$13,889
d, \$11,111

Answer is B and this is their explanation:

PV cash savings/inflows = PV net cash outflows
Annual savings x 3.60 = \$50,000 – \$10,000(0.57)
Annual savings = (\$50,000 – \$5,700)/3.60
Annual savings = \$12,306

#3063405 Guest
Guest

You will be spending \$50,000 now. So, to realize a 12% investment yield, you want to make sure that the present value of the residual value (at a 12% rate) plus the present value of whatever the annual savings will be (at a 12% rate) will equal the initial \$50,000 cost.

Therefore \$50,000 = Present Value of Residual Value + Present Value of Annual Savings

Present Value of Residual Value = Residual Value * PV Factor
Present Value of Residual Value = \$10,000 * 0.57
Present Value of Residual Value = \$5,700

\$50,000 = \$5,700 + Present Value of Annual Savings

Present Value of Annual Savings = 50,000 – 5,700 = \$44,300

Now that we know what the present value of the annual savings is, we need to determine what the annual savings actually is:

Present Value of Annual Savings = Annual Savings * PV Annuity Factor
\$44,300 = Annual Savings * 3.6

Annual Savings = \$44,300 / 3.6 = \$12,305.56

Viewing 2 posts - 1 through 2 (of 2 total)
• You must be logged in to reply to this topic.