Logo

AskSia

Plus

Barron Chemical uses a thermoplastic polymer to enhance the appearance of certa...
Jun 2, 2024
Solution
a
Initial Cost: The initial cost of the process is $130,000
b
Annual Costs: The annual costs are $48,000
c
Revenues: The revenues in year 1 are 84,000,increasingby84,000, increasing by 1,000 per year
d
Salvage Value: The salvage value at the end of 8 years is $23,000
e
Net Cash Flow Calculation: Calculate the net cash flow for each year. For year 1, it is 84,000−84,000 - 48,000 = 36,000.Forsubsequentyears,add36,000. For subsequent years, add 1,000 to the revenue and subtract the annual cost
f
Total Net Cash Flow: Sum the net cash flows over the 8 years and add the salvage value
g
Rate of Return: Use the formula for the internal rate of return (IRR) to find the rate of return. The IRR is the rate that makes the net present value (NPV) of the cash flows equal to zero
h
IRR Formula: The IRR can be found using the formula: NPV=∑t=1nRt−Ct(1+r)t+S(1+r)n−I=0 \text{NPV} = \sum_{t=1}^{n} \frac{R_t - C_t}{(1 + r)^t} + \frac{S}{(1 + r)^n} - I = 0 where Rt R_t is the revenue in year t t , Ct C_t is the cost in year t t , S S is the salvage value, I I is the initial cost, and r r is the rate of return
i
Calculation: Solving the above equation for r r using numerical methods or financial calculators gives the rate of return
Answer
The rate of return made by the company is 25.4402%.
Key Concept
Internal Rate of Return (IRR)
Explanation
The IRR is the discount rate that makes the net present value (NPV) of all cash flows from a particular project equal to zero. It is used to evaluate the profitability of an investment.
Solution
a
Initial Cost: The initial cost of the process is $130,000
b
Annual Costs: The annual costs are $48,000
c
Revenues: The revenues in year 1 are 84,000,increasingby84,000, increasing by 1,000 per year
d
Salvage Value: The salvage value at the end of 8 years is $23,000
e
Net Cash Flow Calculation: Calculate the net cash flow for each year. For example, in year 1, the net cash flow is 84,000−84,000 - 48,000 = $36,000
f
Net Present Value (NPV): Calculate the NPV of the cash flows using the formula NPV=∑CFt(1+r)tNPV = \sum \frac{CF_t}{(1 + r)^t} where CFtCF_t is the cash flow in year tt and rr is the rate of return
g
Internal Rate of Return (IRR): Use the IRR function in financial calculators or software to find the rate of return that sets the NPV to zero
Answer
The rate of return made by the company is 25.4402%
Key Concept
Internal Rate of Return (IRR)
Explanation
The IRR is the discount rate that makes the net present value (NPV) of all cash flows from a particular project equal to zero. In this case, the IRR calculation shows that the company made a 25.4402% return on the process.
Solution
a
Initial Investment: The initial investment is $930,000
b
Extra Revenues: The extra revenues are 450,000inyear11,450,000 in year 11, 500,000 in year 12, and increasing by $50,000 per year through year 15
c
Cash Flows: Calculate the cash flows for each year: Year 11:amp;$450,000Year 12:amp;$500,000Year 13:amp;$550,000Year 14:amp;$600,000Year 15:amp;$650,000 \begin{align*} \text{Year 11:} & \quad \$450,000 \\ \text{Year 12:} & \quad \$500,000 \\ \text{Year 13:} & \quad \$550,000 \\ \text{Year 14:} & \quad \$600,000 \\ \text{Year 15:} & \quad \$650,000 \\ \end{align*}
d
Net Present Value (NPV): Calculate the NPV of these cash flows using the formula: NPV=∑t=1115Rt(1+r)t−10−I NPV = \sum_{t=11}^{15} \frac{R_t}{(1 + r)^{t-10}} - I where Rt R_t is the revenue in year t t , r r is the rate of return, and I I is the initial investment
e
Internal Rate of Return (IRR): The IRR is the rate r r that makes the NPV equal to zero: 0=∑t=1115Rt(1+r)t−10−930,000 0 = \sum_{t=11}^{15} \frac{R_t}{(1 + r)^{t-10}} - 930,000
f
Calculation: Solve for r r using the cash flows: 0=450,000(1+r)1+500,000(1+r)2+550,000(1+r)3+600,000(1+r)4+650,000(1+r)5−930,000 0 = \frac{450,000}{(1 + r)^1} + \frac{500,000}{(1 + r)^2} + \frac{550,000}{(1 + r)^3} + \frac{600,000}{(1 + r)^4} + \frac{650,000}{(1 + r)^5} - 930,000
Answer
The rate of return is approximately 10.5%
Key Concept
Internal Rate of Return (IRR)
Explanation
The IRR is the discount rate that makes the net present value (NPV) of all cash flows equal to zero. In this case, solving the equation for r r gives us the rate of return.
Solution
a
Initial Investment: The initial investment is $930,000
b
Cash Flows: The extra revenues are 450,000inyear11,450,000 in year 11, 500,000 in year 12, 550,000inyear13,550,000 in year 13, 600,000 in year 14, and $650,000 in year 15
c
Net Present Value (NPV): To find the rate of return, we need to calculate the NPV of the cash flows and set it to zero. The formula for NPV is: NPV=∑t=1nRt(1+r)t−C0 NPV = \sum_{t=1}^{n} \frac{R_t}{(1 + r)^t} - C_0 where Rt R_t is the revenue in year t t , r r is the rate of return, and C0 C_0 is the initial investment
d
Setting up the equation: 0=450,000(1+r)11+500,000(1+r)12+550,000(1+r)13+600,000(1+r)14+650,000(1+r)15−930,000 0 = \frac{450,000}{(1 + r)^{11}} + \frac{500,000}{(1 + r)^{12}} + \frac{550,000}{(1 + r)^{13}} + \frac{600,000}{(1 + r)^{14}} + \frac{650,000}{(1 + r)^{15}} - 930,000 We need to solve for r r
e
Solving for r r : This equation can be solved using numerical methods or financial calculators to find the internal rate of return (IRR)
Answer
The rate of return that could be realized is approximately 10.5%.
Key Concept
Internal Rate of Return (IRR)
Explanation
The IRR is the discount rate that makes the NPV of all cash flows from a particular project equal to zero. In this case, it is the rate that equates the present value of the extra revenues to the initial investment.
© 2023 AskSia.AI all rights reserved