Question

Installing Tesla solar panels in a house costs $18,000. It is expected that the average monthly savings will be 1,000 kWh per month. Assuming that the utility company charges 0.2 per $/kWhr.

1. What is the Present worth of this investment for i=6% and N=15 years?
2. A different approach could be to install energy efficient windows and enhance the insulation for $12,000, which would yield average monthly savings of 700 kWh per month. Assuming the same interest rate and time span. What is the present worth of this alternative?
3. Which option would you choose? Why?

Answer 1

1)Here we are required to calculate only the present worth of the investment.

Computation of Cash savings/Year

Average monthly savings of energy=1000Kwh

Yearly savings=12*1000kwh=12,000kwh

Yearly savings in $=Total saving in kwh*rate/kwh

12000kwh*0.2/kwh=$2400

Present value of 15 year savings at the rate of 6% per annum

=Yearly savings*PVAF(at 6%,15 years)

(PVAF calculation

PVAFn/i=∑k=1nC(1+i)k=Ci(1−1(1+i)n)=C(1−(1+i)−ni)C⋅PVAFn/i=∑k=1nC(1+i)k=Ci(1−1(1+i)n)=C(1−(1+i)−ni)

PVAF15/0.06=1(1−(1+0.06)−150.06)=1(1−0.417265060735540.06)=1(9.712248987741)=9.712248987741

In simple you can use your calc to compute PVAF,

Step 1 =Type 1/1.06

Step 2 =Press equal ‘=’ symbol 15 times

Step 3=press GT function in your cal)

Hence Present value of 15 year savings at the rate of 6% per annum

=$2400*9.71225=$23309.4

Present worth of investment=$23309.4

2)Present worth of alternative 2 installing energy efficient window

Computation of Cash savings/Year

Average monthly savings of energy=700Kwh

Yearly savings=12*700kwh=8,400kwh

Yearly savings in $=Total saving in kwh*rate/kwh

=8,400kwh*0.2=$1,680

Present value of 15 year savings at the rate of 6% per annum

=Yearly savings*PVAF(at 6%,15 years)

(PVAF calculation

PVAFn/i=∑k=1nC(1+i)k=Ci(1−1(1+i)n)=C(1−(1+i)−ni)C⋅PVAFn/i=∑k=1nC(1+i)k=Ci(1−1(1+i)n)=C(1−(1+i)−ni)

PVAF15/0.06=1(1−(1+0.06)−150.06)=1(1−0.417265060735540.06)=1(9.712248987741)=9.712248987741

In simple you can use your calculator to compute PVAF,

Step 1 =Type 1/1.06

Step 2 =Press equal( ‘=’ )symbol 15 times

Step 3=press GT function in your calc)

Hence Present value of 15 year savings at the rate of 6% per annum

=$1680*9.71225=$16316.6

Present worth of investment=$16316.58

3)Using present worth you cannot choose an option because we haven’t considered the present value of cash outflow for the both investment. Hence for evaluating both the options we can use NPV method(Net present value metod)

NPV of investment=Present value of cash inflow-Present value of cash outflow

If NPV is +ve accept the project and in case NPV is -ve reject the project

Present value of cash outflow for investment 1=$18000

Present value of cash outflow for investment 2=$12000

NPV of investment 1=$23309.4-$18000=$5309.4

NPV of investment 2=$16316.58-$12000=$4316.58

In both case NPV is +ve so we have to select best alternative out of this,

We can use PROFITABILITY INDEX HERE TO SELECT THE BEST AALTERNATIVE(Other alternatives are ARR & Payback period method)

PROFITABILITY INDEX

PI=Present value of cash inflow/Present value of cash outflow

Alternative 1

PI=23309.4/18000=1.2949:1

Alternative 2

PI=16316.58/12000=1.3597:1

Here profitability index is more for Alternative 2 hence we choose install energy efficient window.