Time Value of Money: What is it and How Does it Work?

Question 1: Future values and annuities 

PV = C/ (1+r) t 

= 10000/1.05 5 

=7.835.26 

You have to pay $12,000 a year in school fees at the end of each of the next six years. If the interest rate is 8%, how much do you need to set aside today to cover these bills? 

P=r(PV)/1-(1+r) -n 

12000*1/0.08(1-0.6302) 

=$55,476 

1.086*(60,476-55,476) 

=7.934 

Question 2: IRR rule 

Calculate the NPV of each project for discount rates of 0%, 10%, and 20%. 

NPV=-C o +c 1 /(1+r)+C 2 /(1+r) 2 +C 3 /(1+r) 3 

Project A NPV 

At 0%= -100+60/(1)+60/(1) 2 +0/(1) 3 = 20 

At 10% = -100+60/(1.1)+60/(1.1) 2 +0/(1.1) 3 = 4.13 

At 20% = -100+60/(1.2)+60/(1.2) 2 +0/(1.2) 3 = -8.33 

Project B NPV 

At 0% =-100+0/(1)+0/(1) 2 +140/(1) 3 = 40 

At 10% =-100+0/(1.1)+0/(1.1) 2 +140/(1.1) 3 = 5.18 

At 20% =-100+0/(1.2)+0/(1.2) 2 +140/(1.2) 3 = -18.98 

	Discount Rate
	0%	10%	20%
NPVA	20	4.13	-8.33
NPVB	40	5.18	-18.98

What is the approximate IRR for each project? 

The approximate IRR for project A is 13% while the approximate IRR for project B is 12. 

In what circumstances should the company accept project A? 

The intersection between NPV A and NPVB when drawn graphically gives a value of about 10.6%. Thus, the company should only accept project A if its NPV has a greater value ( Shaban, Al-Zubi, & Abdallah, 2017) compared to 10.6% and lower than the projects IRR of 13%. 

Calculate the NPV of the incremental investment (B - A) for discount rates of 0%, 10%, and 20%. What can you conclude? 

Project	Co	C1	C2	C3
A	-100	60	60	0
B	-100	0	0	140
B-A	0	-60	-60	140

The discount rate of the NPV is as follows 

	Discounted rate
	0%	10%	20%
NPV (B-A)	+20	1.05	-10.65
IRR (B-A)	10.7

From the results, it will be prudent for the company to accept project A as long as the discount rate is more than 10.7% and less than 13% IRR. Graphically, the incremental investment is higher that the forgone cost of capital 

Question 3: IRR rule 

The problem can be set as follows. The values are in thousands. 

Year projected schedule accelerated shift 

1 250 550 

2 250 650 

3 650 

The incremental analysis is then done as follows 

	C1	C2	C3
Current arrangement	-250	-250	+650
Extra Shift	-550	+650	0
Incremental flows	-300	+900	-650

The approximate incremental flows for the company TTL ship building company are about 21.13% and 78.87%. According to the IRR rule projects should be pursued if the IRR is greater than the minimum cost of capital ( Kulakov & Kastro, 2017) . Thus the range of suggests that the company is better placed to work on extra shift. 

Question 4: Capital Rationing 

From the BGMT Pharmaceuticals projects, 2 can be safely eliminated because it net present value is negative. The other projects can be analyzed by ordering the NPV from the highest to the lowest. The ordering of projects in terms of net present value gives 1, 6, 7, 3, 4, and 5. Taking the first three projects; 1, 6, and 7, the company will have to spend $1,050,000 and thus over budget. As such, the project 7 will be dropped. By dropping project 7, projects 3 and 4 can be added where all the investments can be used. The NPV for all the four projects is 186,000. 

The forgone net present value affects the market value of the company. If there was no constraint in the budget, then the company would have invested in all the independent projects with exception of 2 because of the negative NPV ( Abor, 2017) . The total NPV for projects with positive values is $241,000 while the NPV for the chosen projects adds up to $186,000. Thus the company’s limit cost is $55,000. 

References 

Abor, J. Y. (2017). Evaluating Capital Investment Decisions: Capital Budgeting. In  Entrepreneurial Finance for MSMEs  (pp. 293-320). Palgrave Macmillan, Cham. 

Kulakov, N. Y., & Kastro, A. N. B. (2017). New Applications of the IRR Method in the Evaluation of Investment Projects. In  IIE Annual Conference. Proceedings  (pp. 464-469). Institute of Industrial and Systems Engineers (IISE). 

Shaban, O. S., Al-Zubi, Z., & Abdallah, A. A. (2017). The Extent of Using Capital Budgeting Techniques in Evaluating Manager’s Investments Projects Decisions (A Case Study on Jordanian Industrial Companies).  International Journal of Economics and Finance ,  9 (12), 175.