Question

Suppose an economy is made up of four one-year projects with each project costing $1,000,000.

Project	Future Value ($)
One	1,111,000
Two	1,085,000
Three	1,060,000
Four	1,035,000

1. Assuming investors use the NPV criteria to choose investment projects, how much investment (in millions) will there be if the interest rate is 0.05?  
(If your answer is $1 million, then enter 1.)

2. If interest rates are 0.05 then savings available for investment is $3 million.

What is the difference between Investment (I) and Savings (S) in millions (i.e. I - S) ?  

3. If the country's demand for investment is I = 30 - 181*i, what is investment (I) if i=0.12?  


4. If the country's supply of savings is S = 4 + 104*i, what is savings (S) if i=0.12??  

5. For I and S, in #3 & #4, at what interest rate is I=S?  

Answer 1

Solution:

1. Present value, PV = FV/(1+i)

Net present value = PV - cost of project

Further, investment takes place in the project if net present value is positive. Then,

For project 1, NPV = 1,111,000/(1 + 0.05) - 1000000 = 58,095.24 > 0

For project 2, NPV = 1,085,000/(1 + 0.05) - 1000000 = 33,333.33 > 0

For project 3, NPV = 1,060,000/(1 + 0.05) - 1000000 = 9,523.81 > 0

For project 4, NPV = 1,035,000/(1 + 0.05) - 1000000 = -14,285.71 < 0

So, investment in 3 projects takes place (in last project, NPV is negative). Thus, total investment = total cost in 3 projects = 3*$1m = $3m

2. At interest rate of 0.05, S = $3m

So, I - S = $3m - $3m = 0

3. With country's demand for investment as I = 30 - 181*i

If i = 0.12, I = 30 - 181*0.12

I = 30 - 21.72 = $8.28m

4. With country's savings function as S = 4 + 104*i

if i = 0.12, S = 4 + 104*0.12

S = 4 + 12.48 = $16.48m

5. Finding i for which I = S

30 - 181*i = 4 + 104*i

30 - 4 = i*(104 + 181)

i = 26/285 = 0.0912

So, for interest rate of 9.12%, S = I