The following are the investment and operating costs for two machines, J and K.
Year: 0, 1, 2, 3
J: 11000, 1200, 1300
K: 13000, 1200, 1300, 1400
The WACC is 10.5%. How do I use the WACC to determine which machine is a better buy?
i=10.5%=.105
n=2 for machine J, =3 for machine K
We assume machine J lasts 2 years with no salvage value, same for machine K, but three years.
Case J:
PV=-11000-1200/(1.105)-1300/1.105^2=
=-13150.65
annual expense over 2 years
A=P*(A/P,10.5%,3)
=-13150.65*((i*(1+i)^n)/((1+i)^n-1))
=-13150.65*((.105(1.105^2)/(1.105^2-1)
=-13150.65*0.580059
=-$7628.16
Case K:
PV=-13000-1200/1.105-1300/1.105^2-1400/1.105^3
=-16188.28
annual expense over 3 years
A=P*(A/P,10.5%,3)
=-16188.28*((i*(1+i)^n)/((1+i)^n-1))
=-16188.28*((.105(1.105^3)/(1.105^3-1)
=-16188.28*0.40566
=-$6566.92
Since annual expense for machine K is lower, it is a better buy.
Another way to do this is compare the present values of buying 3 machine J with the PV of 2 machine K (total 6 years in each case).
It is less realistic because the machines may not cost the same 2,3 or 4 years from now.
Here it is anyway:
Machine J:
PV=-13150.652-13150.652/1.105^2-13150.652/1.105^4
=-32741.43
Machine K:
PV=-16188.28-16188.28/1.105^3
=-28186.42
Again, Machine K has a lower (negative) cash flow over 6 years.
Many thanks for your help again, MathMate!
To determine which machine is a better buy, you need to calculate the Net Present Value (NPV) for each machine using the Weighted Average Cost of Capital (WACC) as the discount rate. The NPV represents the present value of all future cash flows associated with an investment.
Step 1: Calculate the present value of cash flows for each machine.
For machine J:
Year 0: Present Value = $11,000 / (1 + WACC)^0 = $11,000
Year 1: Present Value = $1,200 / (1 + WACC)^1
Year 2: Present Value = $1,300 / (1 + WACC)^2
Year 3: Present Value = $0 (no cash flow in Year 3)
For machine K:
Year 0: Present Value = $13,000 / (1 + WACC)^0 = $13,000
Year 1: Present Value = $1,200 / (1 + WACC)^1
Year 2: Present Value = $1,300 / (1 + WACC)^2
Year 3: Present Value = $1,400 / (1 + WACC)^3
Step 2: Calculate the sum of the present values for each machine.
For machine J:
NPV_J = Present Value of Year 0 + Present Value of Year 1 + Present Value of Year 2 + Present Value of Year 3
For machine K:
NPV_K = Present Value of Year 0 + Present Value of Year 1 + Present Value of Year 2 + Present Value of Year 3
Step 3: Compare the NPVs of the two machines.
If NPV_J > NPV_K, then machine J is a better buy.
If NPV_J < NPV_K, then machine K is a better buy.
If NPV_J = NPV_K, then both machines have the same value.
By comparing the NPVs calculated for each machine, you can determine which one is a better buy based on their respective cash flows and the WACC.
To determine which machine is a better buy, you need to calculate the Net Present Value (NPV) of each investment using the Weighted Average Cost of Capital (WACC).
1. Calculate the Discounted Cash Flow (DCF) for each machine:
- For Machine J:
- Year 0: No cash flow, so no calculation is necessary.
- Year 1: Cash inflow of $1,200 discounted by (1 + WACC)^1.
- Year 2: Cash inflow of $1,300 discounted by (1 + WACC)^2.
- Year 3: Cash inflow of $1,300 discounted by (1 + WACC)^3.
- For Machine K:
- Year 0: No cash flow, so no calculation is necessary.
- Year 1: Cash inflow of $1,200 discounted by (1 + WACC)^1.
- Year 2: Cash inflow of $1,300 discounted by (1 + WACC)^2.
- Year 3: Cash inflow of $1,400 discounted by (1 + WACC)^3.
2. Apply the formula for NPV calculation:
NPV = Cash Flow / (1 + WACC)^n
3. For each machine, sum up the discounted cash flows to calculate the NPV:
- For Machine J: NPV_J = 1200 / (1 + 0.105)^1 + 1300 / (1 + 0.105)^2 + 1300 / (1 + 0.105)^3
- For Machine K: NPV_K = 1200 / (1 + 0.105)^1 + 1300 / (1 + 0.105)^2 + 1400 / (1 + 0.105)^3
4. Compare the NPVs of both machines. If the NPV is positive, it indicates that the machine is generating a positive return. The higher the NPV, the better the investment.
By comparing the NPVs of Machines J and K, you can determine which machine is a better buy based on their respective NPV values.