Question

5 - 100 florida power and light has committed to building a solar power plant. joanne, an ie working for fpl, has been tasked with evaluating the three current designs. fpl uses an interest rate of 10% and a 20 - year horizon.
design 1: flat solar panels
a field of “flat” solar panels angled to best catch the sun will yield 2.6 mw of power and will cost $87 million initially with first - year operating costs at $2 million, growing $250,000 annually. it will produce electricity worth $6.9 million the first year, and will increase by 8% each year thereafter.
design 2: mechanized solar panels
a field of mechanized solar panels rotates from side to side so that they are always positioned parallel to the sun’s rays, maximizing the production of electricity. this design will yield 3.1 mw of power and will cost $101 million initially with first - year operating costs at $2.3 million, growing $300,000 annually. it will produce electricity worth $8.8 million the first year and will increase 8% each year thereafter.
design 3: solar collector field
this design uses a field of mirrors to focus the sun’s rays onto a boiler mounted in a tower. the boiler then produces steam and generates electricity the same way a coal - fired plant operates. this system will yield 3.3 mw of power and will cost $91 million initially with first - year operating costs at $3 million, growing $350,000 annually. it will produce electricity worth $9.7 million the first year and will increase 8% each year thereafter.

Explanation:

Step1: Recall the net - present - value (NPV) formula

The NPV formula for a cash - flow series $C_t$ over $n$ years with an interest rate $i$ is $NPV=-C_0+\sum_{t = 1}^{n}\frac{C_t}{(1 + i)^t}$. For a growing cash - flow series with initial value $A$ and growth rate $g$, the present value of the series over $n$ years is $PV=\sum_{t = 1}^{n}\frac{A(1 + g)^{t-1}}{(1 + i)^t}$. When $i
eq g$, $PV=\frac{A}{i - g}(1-(\frac{1 + g}{1 + i})^n)$. When $i = g$, $PV=\frac{nA}{1 + i}$.

Step2: Calculate NPV for Design 1

Initial cost $C_0 = 87$ million.
First - year net cash - flow $A_1=6.9 - 2=4.9$ million, $g = 8\%=0.08$, $i = 10\%=0.1$, $n = 20$.
The present value of the net cash - flow series $PV_{1}=\frac{4.9}{0.1 - 0.08}(1-(\frac{1 + 0.08}{1 + 0.1})^{20})$.
$PV_{1}=\frac{4.9}{0.02}(1 - 0.676347)= \frac{4.9}{0.02}\times0.323653=79.392985$ million.
$NPV_1=-87 + 79.392985=-7.607015$ million.

Step3: Calculate NPV for Design 2

Initial cost $C_0 = 101$ million.
First - year net cash - flow $A_1=8.8 - 2.3 = 6.5$ million.
The present value of the net cash - flow series $PV_{2}=\frac{6.5}{0.1 - 0.08}(1-(\frac{1 + 0.08}{1 + 0.1})^{20})$.
$PV_{2}=\frac{6.5}{0.02}(1 - 0.676347)=\frac{6.5}{0.02}\times0.323653 = 105.167225$ million.
$NPV_2=-101+105.167225 = 4.167225$ million.

Step4: Calculate NPV for Design 3

Initial cost $C_0 = 91$ million.
First - year net cash - flow $A_1=9.7 - 3=6.7$ million.
The present value of the net cash - flow series $PV_{3}=\frac{6.7}{0.1 - 0.08}(1-(\frac{1 + 0.08}{1 + 0.1})^{20})$.
$PV_{3}=\frac{6.7}{0.02}(1 - 0.676347)=\frac{6.7}{0.02}\times0.323653=108.742255$ million.
$NPV_3=-91 + 108.742255=17.742255$ million.

Answer:

Design 3 has the highest NPV of approximately $\$17.74$ million, so Design 3 is the best design.