home / study / business / economics / questions and answers / 7.1 calculate the
ID: 2760502 • Letter: H
Question
home / study / business / economics / questions and answers / 7.1 calculate the internal rate of return (irr) ... Your question has been posted. We'll notify you when a Chegg Expert has answered. Post another question. Question Edit question 7.1 Calculate the Internal Rate of Return (IRR) for an investment in a 400-MW power plant with an expected life of 30 years. This plant costs 1200 $/kW to build and has a heat rate of 9800 Btu/kWh. It burns a fuel that costs 1.10 $/MBtu. On average, it is expected to operate at a maximum capacity for 7446 h per year and sell its output at an average price of 31 $/MWh. What should be the average price of electrical energy if this investment is to achieve a MARR of 13%?What would be the Internal Rate of Return of the unit of Problem 7.1 if the price of electrical energy was 35 $/MWh during the first 10 years of the expected life of the plant before dropping to 31 $/MWh? What would be the value to the Internal Rate of Return if this price was 31 $/MWh during the first 20 years and 35 $/MWh during the last 10 years. Compare these results with the Internal Rate of Return calculated in Problem 7.1 and explain the differences.
Explanation / Answer
fuel burn cost=1.10 $/MBtu=0.000001*1.10 $/Btu
cost of producing power per year=C=(9800 Btu/kWh)*(0.000001*1.10 $/Btu)*(7446 h)=80.26788 $/kW
Price of power output=31 $/MWh=(31*7446/1000)$/kW=230.826 $/kW
Net profit=230.826 -80.26788 $/kW=150.55812 $/kW
FOr IRR, Present value of profits= (150.55812 /IRR)*(1-1/(1+IRR)^30)=1200
@IRR=12%,LHS=(150.55812 /.12)*(1-1/(1+.12)^30)=1212.77
@IRR=12.5%,LHS=(150.55812 /.125)*(1-1/(1+.125)^30)=1169.29
@IRR=12.1%,LHS=(150.55812 /.121)*(1-1/(1+.121)^30)=1203.1
@IRR=12.12%,LHS=(150.55812 /.1212)*(1-1/(1+.1212)^30)=1202
@IRR=12.15%,LHS=(150.55812 /.1215)*(1-1/(1+.1215)^30)=1199.5
@IRR=12.14%,LHS=(150.55812 /.1214)*(1-1/(1+.1214)^30)=1200
Therefore the the Internal Rate of Return (IRR) for the investment is 12.14%.
Let the Price of power output=X $/kW
Net profit=X-80.26788 $/kW
THerefore preset value of Net profits after 30 years =((X-80.26788) /.13)*(1-(1/(1.13)^30)=7.49565*(X-80.26788)
7.49565*(X-80.26788)=1200 to achieve a MARR of 13%.
=>X=(1200/7.49565)+80.26788=240.36 $/kW or the price=(240.36*1000/7446)$/MWh=32.38 $/MWh
Therefore the average price of electrical energy if this investment is to achieve a MARR of 13% should be 32.38 $/MWh.
Price of power output=35 $/MWh=(35*7446/1000)$/kW=260.61 $/kW for 10 years
Price of power output=31 $/MWh=(31*7446/1000)$/kW=230.826 $/kW after 10 years
Profit for first 10 years=260.61 -80.26788 $/kW=180.34212 $/kW
Net profit after 10 years=230.826 -80.26788 $/kW=150.55812 $/kW
Present value of profits= (180.34212/IRR)*(1-1/(1+IRR)^10)+(150.55812 /IRR)*(1-1/(1+IRR)^20)*(1/(1+IRR)^10)=1200
For IRR=15%=0.15,Present value of profits=(180.34212/0.15)*(1-1/(1+0.15)^10)+(150.55812 /0.15)*(1-1/(1+0.15)^20)*(1/(1+0.15)^10)=1138
For IRR=14%=0.14,Present value of profits=(180.34212/0.14)*(1-1/(1+0.14)^10)+(150.55812 /0.14)*(1-1/(1+0.14)^20)*(1/(1+0.14)^10)=1209.66
For IRR=14.2%=0.142,Present value of profits=(180.34212/0.142)*(1-1/(1+0.142)^10)+(150.55812 /0.142)*(1-1/(1+0.142)^20)*(1/(1+0.142)^10)=1194.67
For IRR=14.1%=0.141,Present value of profits=(180.34212/0.141)*(1-1/(1+0.141)^10)+(150.55812 /0.141)*(1-1/(1+0.141)^20)*(1/(1+0.141)^10)=1202
For IRR=14.12%=0.1412,Present value of profits=(180.34212/0.1412)*(1-1/(1+0.1412)^10)+(150.55812 /0.1412)*(1-1/(1+0.1412)^20)*(1/(1+0.1412)^10)=1200.6
Therefore IRR=14.12% if the price of electrical energy was 35 $/MWh during the first 10 years of the expected life of the plant before dropping to 31 $/MWh.
Price of power output=35 $/MWh=(35*7446/1000)$/kW=260.61 $/kW for last 10 years
Price of power output=31 $/MWh=(31*7446/1000)$/kW=230.826 $/kW first 20 years
Profit for last 10 years=260.61 -80.26788 $/kW=180.34212 $/kW
Net profit first 20 years=230.826 -80.26788 $/kW=150.55812 $/kW
Present value of profits= (180.34212/IRR)*(1-1/(1+IRR)^10)*(1/(1+IRR)^20)+(150.55812 /IRR)*(1-1/(1+IRR)^20)=1200
For IRR=14%=0.14,Present value of profits=(180.34212/.14)*(1-1/(1+.14)^10)*(1/(1+.14)^20)+(150.55812 /.14)*(1-1/(1+.14)^20)=1065.6
For IRR=12%=0.14,Present value of profits=(180.34212/.12)*(1-1/(1+.12)^10)*(1/(1+.12)^20)+(150.55812 /.12)*(1-1/(1+.12)^20)=1230.2
For IRR=12.2%=0.14,Present value of profits=(180.34212/.122)*(1-1/(1+.122)^10)*(1/(1+.122)^20)+(150.55812 /.122)*(1-1/(1+.122)^20)=1211.7
For IRR=12.3%=0.14,Present value of profits=(180.34212/.123)*(1-1/(1+.123)^10)*(1/(1+.123)^20)+(150.55812 /.123)*(1-1/(1+.123)^20)=1203
For IRR=12.36%=0.14,Present value of profits=(180.34212/.1236)*(1-1/(1+.1236)^10)*(1/(1+.1236)^20)+(150.55812 /.1236)*(1-1/(1+.1236)^20)=1197
For IRR=12.33%=0.14,Present value of profits=(180.34212/.1233)*(1-1/(1+.1233)^10)*(1/(1+.1233)^20)+(150.55812 /.1233)*(1-1/(1+.1233)^20)=1200 therefore the IRR is 12.33% if this price was 31 $/MWh during the first 20 years and 35 $/MWh during the last 10 years.
Related Questions
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.