Question

Consider an investment that pays $41.49 in year 1, and then stabilizes and pays $4.81 every year forever after that (the first cash flow is in year 2) This firm does not intend to grow and has an interest rate (required rate of return) of 5%. What is the present value of this investment opportunity? Give your answer to two decimals

Answer 1

horizon value = perpetual payment/rate of return = 4.81/0.05=96.2

Value in year 1 = horizon value+Cash flow in year 1 = 41.49+96.2=137.69

Future value = present value*(1+ rate)^time

137.69 = Present value*(1+0.05)^1

Present value = 131.133

Answer 2

Given:

• Cash flow in Year 1 (CF₁): $41.49

• Perpetual cash flow from Year 2 onward (CF): $4.81 per year

• Discount rate (r): 5% or 0.05

• 
  

Step 1: Present Value of Year 1 Cash Flow

The present value of the cash flow received in Year 1 is simply its discounted value:

$$P{V}_{\text{Year 1}}=\frac{C{F}_1}{(1+r)}=\frac{41.49}{1.05}\approx 39.51$$

Step 2: Present Value of the Perpetuity (Starting in Year 2)

The perpetuity formula gives the value one year before the first cash flow, which is Year 1 in this case (since the perpetuity starts in Year 2):

$$P{V}_{\text{Perpetuity at Year 1}}=\frac{CF}{r}=\frac{4.81}{0.05}=96.20$$

Now, discount this value back to the present (Year 0):

$$P{V}_{\text{Perpetuity at Year 0}}=\frac{96.20}{(1+r)}=\frac{96.20}{1.05}\approx 91.62$$

Step 3: Total Present Value

Add the present values of the two components:

$$P{V}_{\text{Total}}=P{V}_{\text{Year 1}}+P{V}_{\text{Perpetuity at Year 0}}=39.51+91.62=131.13$$

Answer:

The present value of the investment opportunity is $\boxed{{\displaystyle 131.13}}$