Question

Excel Hydro took a loan contract which requires a payment of $40 million-plus interest two years after the contract's date of issue. The interest rate on the $40 million face value is 9.6% compounded quarterly. Before the maturity date, the original lender sold the contract to a pension fund for $43 million. The sale price was based on a discount rate of 8.5% compounded semi-annually from the date of sale.

Excel Hydro is also considering building a nuclear power plant, which will be ready for production in 2030. The country's governing body is also considering a decommissioning liability law for the operator to put aside $1 million every month towards decommissioning cost. If the production life of the plant is 60 years and the operator puts the money at the end of the month in a savings account, earning 7.25% compounded monthly.

During the 60 years of the production life of the plant, the operator will put $1 million at the end of the month in a savings account, earning 7.25% compounded monthly. At the end of the production life of the plant, there are no more contributions and the money is expected to grow at the rate of 6% compounded quarterly for the next 30 years.

1.       How many months before the maturity date did the sale take place?

2.       What will be the value of the decommissioning fund after 60 years of production?

3.       What will be the value of the decommissioning fund in 2120?

4.       How much interest is included in the future value in 2120?

Answer 1

Answer to question No. 1 >

Loan amount Payable by Excel Hydro after 2 years = $ 40 million x ( 1+ 9.60%/4)^2*4

= 40 million x ( 1 + 2.40%) ^ 8 = $ 48.357 million

This $ 48.357 million is receivable by the lender.

Now, given that lender has sold this loan receivable asset at $ 43 million to pension fund.

Required how many months before the maturity did the sale take place = By solving the equation as below :

or, $43 million x ( 1 + 8.5%/2)^ n*2 = $48.357 million

or, $43 million x (1+4.25%) ^2n = $ 48.357 million

Solving the above,

n = 2.82 years = 17 months approx. (answer)

Answer to question No. 2 >

Value of Decommissioning Fund after 60 years = Type in excel the following :

PMT = 1,000,000

NPER = 60 YEARS * 12 MONTHS =720

RATE = 7.25%/12 = 0.6042%

PV = 0

TYPE = 0

FORMULAE = FV(RATE,NPER,PMT, PV, TYPE) = $12.492 Billion (answer)

Answer to Question No. 3 >

Value of Fund in 2120 = $ 12.492 Billion (as above) * (1 + 6%/4) ^ 30 * 4

= $ 74. 57 Billion

Answer to Question No. 4 >

Total Principal = $ 1 million p.m. x 12 months p.y. x 60 years = $ 720 million

Total Interest (for period 2030 to 2120) = $ 74.57 billion - 0.72 billion

= $ 73.85 billion

Total Interest (for period 2090 to 2120) = $ 74.57 billion - $ 12.492 billion = $ 62.08 billion