Question

please don't do it by excel, do it manually and show work!

1. A manufacturing company decides to buy solar cells in anticipation of rising electricity costs. The company is modeling its purchase to save it $20,000 for the first year, and this saving increases 5% each year for the next 20 years as the solar cells generate enough electricity to compensate for the rising power bills. If the expected rate of return for the company equals 8%, what is the maximum amount of initial investment that makes this a desirable and profitable project? (assume the solar cells are maintenance free for the next 20 years, but will be salvaged after that and company recovers no money from salvaging them)

2. If for the problem described above, the solar cells supplier charges the purchasing company $200 annually as a service charge to do the maintenance and repair, should a technical problem arise. What will be the maximum initial investment by the company to make the project profitable?

Answer 1

1. The manufacturing company would save $20,00 for the first year and then this saving would increase by 5% for next 20 years. SO we will discount 20000 for first year and present value of growing annuity amount at the end of 1 year also needs to be discounted to todays value.

PV = 20,000 / (1+r) + [PVGA of 20000 ( 5%,8%,20)] / (1+r)

PVGA = P / ( r - g) * [ 1 - ( (1+g) / (1+r) ) ⁿ ]

PVGA = 20000 / ( 0.08 - 0.05) [ 1 - ( ( 1+ 0.05) / (1+0.08) )²⁰ ]

PVGA = 20000 / ( 0.08 - 0.05) [ 1 - ( ( 1+ 0.05) / (1+0.08) )²⁰ ]

PVGA = 666666.7 * [ 1 - 0.56926 ]

PVGA = 666666.7 * 0.43074

PVGA = 287159.82

Putting in the first equation

PV = 20000 / ( 1+ 0.08) + 287159.82 / 1.08

PV = 18518.52 + 265888.7

PV = $284407.2

The maximum amount of investment for this to be a desirable one is $284407.2

2. Now an additional cost of $200 needs to be incurred for the first yea and next 20 years. so total 21 years.

present value of this extra cost = present value annuity of $200

PV = P*[ 1 - ( 1 +r )^{-n ] / r}

PV = 200*[ 1 - (1.08)^-21 ] / 0.08

PV = 200 * [ 1 - 0.198656 } / 0.08

PV = 200 * 0.801344 / 0.08

PV = $2003.36

Therefore maximum initial investment should be $284407.2 + $2003.36 = $286410.56.