Question

Question The developer and owner of a shopping mall is planning to install solar PV panels on the roof top. Project Costs: The 100-kw system will cost $225,000 to install on 600 m2 of space available on the roof top. It will have a useful life 20 years and a salvage value of $2,000. Annual operations and maintenance cost will be $1,500. Energy output: Based on Singapore weather conditions, the system is capable of producing 170,000 kwh of electricity in the first year of operation. However, this output will degrade at a rate of 2% per year through its useful life. The electricity produced will be sold to either the shopping mall's tenants or to the power grid at 18 cents per kwh. Project Financing: 60% of the initial system cost will be financed via a 5-year bank loan at an interest rate of 5% per year. The loan will be repaid with 5 equal end-of-year payments starting at the end of the first year. The other 40% of the initial project cost will be financed with company's equity capital. The company computes the WACC and determines that MARR should be 10% for the purpose of evaluating the feasibility of this project (a) What is the annual repayment amount for the bank loan? (1 mark) (b) What is the Present Worth of the project? Is the project financially feasible? (3 marks) (c) What is the IRR of the project? (3 marks) (d) The Levelized Cost of Energy (LCOE) is the "average" equivalent cost of installing and operating an energy generation asset, per unit of total energy generated over the useful life. Equivalently, LCOE is the constant sale price of electricity generated that makes PW = 0. Determine the LCOE of the proposed solar PV project in cents/kwh. (3 marks)

Answer 1

SOLUTION:-

Please refer to the Cash flows & calculations shown in the following :

G H I 5 Initial cost MARR, Salvage value Annual O&M costs Electricity price/kw 225000 10% 2000 1500 0.18 Loan duration (years) Interest rate Annual repayment 5% $-31,181.60 =PMT(G3,5,60%*D1) 0 6 18 19 20 Year Initial capital outlay for replacement Cost of new furnace Net initial outlay $ $ 2,25,000.00 2,25,000.00 170000 Operating cash flows Maintenance Costs Output Price per kwh Net earnings from selling the power Net operating cash flow (=Savings- Operating costs) 1,500 $ 1,500 $ 166600163268 0.18 $ 0.18 $ 30,600.0 $ 29,988.0 $ 29,100 $ 28,488 $ 1,500 $ 1,500 $ 1,500 160003 156803 0.18 $ 0.18 $ 0.18 29,388.2 $ 28,800.5 $ 28,224.5 27,888 $ 27,300 $ 26,724 $ 1,500 $ 1,500 $ 1,500 $ 1,500 153667 120585 118173 1 15810 $ 0.18 $ 0.18 $ 0.18 $ 0.18 $ 27,660.0 $ 21,705.2 $ 21,271.1 $ 20,845.7 $ 26,160 $ 20,205 $ 19,771 $ 19,346 Cash flow from salvage value 2000 $ Net Cash flows PV of cash flows (=CF/(1+r)^year) -2,25,000 -225000 29,100 $ 28,488 $ 26454.55 23543.80 27,888 $ 20952.85 27,300 $ 26,724 $ 26,160 $ 20,205 $19,771 $ 21,346 18646.59 16593.79 14766.62 3634.09 3232.74 3172.91 Present Worth IRR -7,778.15 -Sum of all PVS 9.4% =IRR(D18:X18,10%) To calculate the LCOE = Sum of PV costs over all the years / Sum of PV of electrical output every year Total costs for each year $ 2,25,000.00 $ 1,500.00 $1,500.00 $ 1,500.00 $ 1,500.00 $1,500.00 PV of costs ($) 225000 1363.64 1239.67 1126.97 1024.52 931.38 PV of power output (kWh) 0.00 154545.45 137685.95 122665.66 109283.96 97362.07 LCOE= 0.1861 = Sum of PV costs over all the years / Sum of PV of electrical output every year $1,500.00 846.71 86740.75 $1,500.00 269.79 21688.22 $1,500.00 245.26 19322.23 $ -500.00 -74.32 17214.35

(please note some years in between are not shown as they follow the same cash flow pattern & formulas)

To calculate the Loan repayment, use the PMT function of Excel (or financial calculator) with the inputs as shown.

To calculate LCOE, we add all costs for each year as is done in row 29 (Note that salvage value will need to be subtracted from the costs in the 20th year)

Similarly, we find the PV of electricity generation by discounting that year's output by (1+10%)^year.

Finally, we divide the resulting values as shown to get the LCOE= 18.61 cents

If you have any doubts, please let me know in the comments.