Question

1. A new furnace for your small factory will cost $27,000 to install and will require ongoing maintenance expenditures of $1,500 a year.2. However, since it will be much more efficient than the furnace you have now, it will reduce your consumption of heating oil by 2,400 gallons per year.3. Heating oil is expected to cost on average $3.50 per gallon in the upcoming year, and that price is expected to increase by $0.50 each year for the two years that follow.From that point onwards, oil prices are expected to stabilize for the foreseeable future.4. The furnace will last for 20 years, at which point it will need to be replaced and will have no salvage value.The discount rate is 8%.a) What is the payback period of the investment?b) What is the discounted payback period of the investment?c) What is the NPV of the investment in the furnace?

Answer 1

Answer:

payback 3.29 years

NPV 87,158.55

Explanation:

PO 27,000

Cash flow saving Y1

2400 x 3.5 = 8,400

expenditures (1,500)

net savings   6,900

Cash flow saving Y2

The price will increase 0.5

6,900 + 2,400 x 0.5 = 8,100

Cash flow saving Y3 to Y20

The price will increase 0.5

8,100 + 2,400 x 0.5 = 9,300

We have an annuity of 18 years for 9,300 cash

And then we have a cash flow of 6,900

and another of 8,100

$C \times \frac{1-(1+r)^{-time} }{rate} = PV$

C = 9,300

r = 8%

time = 18

$9,300 \times \frac{1-(1+0.08)^{-18} }{0.08} = PV$

PV =  87,158.55

Now this values are years into the future, so we need to bring them to present day.

$\frac{Principal}{(1 + rate)^{time} } = PV$

year 1 principal 6,900

6,900/1.08 = 6,388.89

year 2 principal 8,100

$\frac{8,100}{(1 + 0.08)^{2} } = PV$

PV= 5,915.64

year 3 annuity 87,158.55

$\frac{87,158.55}{(1 + 0.08)^{3} } = PV$

PV= 69,189.27

cash flow - investment = net present value

69,189.27 + 5,915.64 + 6,388.89 - 27,000 = 54,493.8

The payback will be the time perdion when the project recovers it initial cost:

we first add the income from the irregular years and subtract from the investment

6,900 + 8,100 = 15,000

27,000 - 15,000 = 12,000

then we use the general formula investment/cash flow per year

12,000/9,300 = 1.29

the project need the first two years and then 1.29 years

2 + 1.29 = 3.29 years