+598 Focus Drilling is creating an expansion. The expansion will occur over 4 years and is expected to require $2.8 million.
Management has developed a payment plan for carrying out this expansion. The plan requires a cash input of $300,000 now, $700, 000 one year from now, $800,000 two years from now, and finally, $1,000,000 four years from now.
he Treasurer has predicted interest rates over the next four years to be as follows:
Year 1: interest rate of 4.5% p.a. compounded semi-annually
Year 2: interest rate of 5.0% p.a. compounded semi-annually
Year 3: interest rate of 5.0% p.a. compounded semi-annually
Year 4: interest rate of 5.5% p.a. compounded semi-annually
Since the Treasurer’s investment plan has a guaranteed rate for five years, suppose the company decided to delay the expansion for twelve months to take advantage of this fact. The payment plan to fund the expansion would retain the same payment schedule. However, the final payment in the last year would increase by 10%, due to projected increase in construction costs.
1. Twelve months from now, what is the total of the value of the required cash payments? Show your calculations.
Any help with steps would be greatly appreciated, thanks
+495 This is not my best area of math, so don't take my word for it, but here's what I got:
I think the interest rate applies to amount of money that is borrowed.
Then apply the interest on what is borrowed as often as needed (2 times a year) but subtract
That means the amount of money borrowed at each year is:
0) (start) 2,800,000 - 300,000 = 2,500,000
2,500,000*1.045^2 = 2,730,062.5
1) 2,730,062.5 - 700,000 = 2,030,062.5
2,030,062.5*1.05^2 = 2,238,143.91
2) 2,238,143.91 - 800,000 = 1,438,143.91
1,438,143.91*1.05^(2/0.5) = 1,748,072.91
4) 1,748,072.91 - 1,000,000 = 748,072.91
748,072.91*1.055^2 = 832,623.85
Then it says at year 5, increase final payment by 10%.
5) 832,623.85* 110% = 915,886.24
I'm guessing this means the final payment would be $915,886.24
But it says twelve months from now, so maybe it wants you to say what is owed after the first year?
If that's the case,it would be $2,730,062.5 before making the prescheduled payment of $700,000.
I don't know for sure, and check my work.
+598 Hey LambLamb,
Appreciate the help thus far. I will revise your work that you have giving me. I also posted this same question again with a couple other following question on the forum. If you want to look at that, that would be great.
Thanks
If the company decides to delay the expansion for 1 year, then this means that the whole of reserve fund will be invested for 1 full year at 5.2% comp. quarterly.
This would come to $2,737,859.32 - $2,6000,000=$137,859.32 This is additional cash that the company has earned in 1 year. This new cash will continue to earn interest for another 4 years, which will be worth $169,506.86. This is in addition to the surplus calculated in question #3.
From the calculations here and in the previous question, the last payment will increase from a $1,000,000 to $1,100,000, which will be subtracted from the final amount.
Since the payments are delayed for 1 year, then their PV, which we calculated in question #1 will be projected into 1 year from now at the assumed rate of 4.5% comp.S.A., which will come to $2,612,928.15.
