Solve the following by the Trial and Error method as outlined in the text and ex

Question

Solve the following by the Trial and Error method as outlined in the text and explained in the recording (Excel solutions will not be accepted). Your solution must show all equations with the factor values inserted (12), and the answer (3). The first cost of a product sold by JadaTech Inc. was $378,000. It has annual costs of $147,000 and annual revenues of $264,000. A salvage value of $99,000 was realized when the product was discontinued after 8 years. What rate of return did JadaTech make on the product?

Explanation / Answer

The Rate of Return can be calculated with the use of following formula:

NPV = 0 = Cash Flow Year 0 + Cash Flow Year 1/(1+Rate of Return )^1 + Cash Flow Year 2/(1+Rate of Return )^2 + Cash Flow Year 3/(1+Rate of Return )^3 + Cash Flow Year 4/(1+Rate of Return )^4 + Cash Flow Year 5/(1+Rate of Return )^5 + Cash Flow Year 6/(1+Rate of Return )^6 + Cash Flow Year 7/(1+Rate of Return )^7 + Cash Flow Year 8/(1+Rate of Return )^8

________

Here, Cash Flow Year 0 = -$378,000

Annual Cash Flow (Year 1 - Year 7) = 264,000 - 147,000 = $117,000

Terminal Year Cash Flow (Year 8) = 117,000 + 99,000 = $216,000

________

Now, we can use Trial and Error Method to arrive at Rate of Return. We will calculate NPV at different Rates of Return as follows:

26%

NPV = -378,000 + 117,000/(1+26%)^1 + 117,000/(1+26%)^2 + 117,000/(1+26%)^3 + 117,000/(1+26%)^4 + 117,000/(1+26%)5 + 117,000/(1+26%)^6 + 117,000/(1+26%)^7 + 216,000/(1+26%)^8 = $16,748.67

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27%

NPV = -378,000 + 117,000/(1+27%)^1 + 117,000/(1+27%)^2 + 117,000/(1+27%)^3 + 117,000/(1+27%)^4 + 117,000/(1+27%)5 + 117,000/(1+27%)^6 + 117,000/(1+27%)^7 + 216,000/(1+27%)^8 = $5,930.72

___

28%

NPV = -378,000 + 117,000/(1+28%)^1 + 117,000/(1+28%)^2 + 117,000/(1+28%)^3 + 117,000/(1+28%)^4 + 117,000/(1+28%)5 + 117,000/(1+28%)^6 + 117,000/(1+28%)^7 + 216,000/(1+28%)^8 = -$4,393.17

___

As the NPV gets convered from a positive value at 27% to a negative value at 28%, the rate of return will lie between 27% to 28%. We will continue with the process of trying other rates till the time the NPV becomes zero.

27.50%

NPV = -378,000 + 117,000/(1+27.50%)^1 + 117,000/(1+27.50%)^2 + 117,000/(1+27.50%)^3 + 117,000/(1+27.50%)^4 + 117,000/(1+27.50%)5 + 117,000/(1+27.50%)^6 + 117,000/(1+27.50%)^7 + 216,000/(1+27.50%)^8 = $708.89

___

27.60%

NPV = -378,000 + 117,000/(1+27.60%)^1 + 117,000/(1+27.60%)^2 + 117,000/(1+27.60%)^3 + 117,000/(1+27.60%)^4 + 117,000/(1+27.60%)5 + 117,000/(1+27.60%)^6 + 117,000/(1+27.60%)^7 + 216,000/(1+27.60%)^8 = -$320.99

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As the NPV gets convered from a positive value at 27.50% to a negative value at 27.60%, the rate of return will lie between 27.50% to 27.60%. We will continue with the process of trying other rates till the time the NPV becomes zero.

27.55%

NPV = -378,000 + 117,000/(1+27.55%)^1 + 117,000/(1+27.55%)^2 + 117,000/(1+27.55%)^3 + 117,000/(1+27.55%)^4 + 117,000/(1+27.55%)5 + 117,000/(1+27.55%)^6 + 117,000/(1+27.55%)^7 + 216,000/(1+27.55%)^8 = $193.36

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27.56%

NPV = -378,000 + 117,000/(1+27.56%)^1 + 117,000/(1+27.56%)^2 + 117,000/(1+27.56%)^3 + 117,000/(1+27.56%)^4 + 117,000/(1+27.56%)5 + 117,000/(1+27.56%)^6 + 117,000/(1+27.56%)^7 + 216,000/(1+27.56%)^8 = $90.39

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27.57%

NPV = -378,000 + 117,000/(1+27.57%)^1 + 117,000/(1+27.57%)^2 + 117,000/(1+27.57%)^3 + 117,000/(1+27.57%)^4 + 117,000/(1+27.57%)5 + 117,000/(1+27.57%)^6 + 117,000/(1+27.57%)^7 + 216,000/(1+27.57%)^8 = -$12.52

As the NPV gets convered from a positive value at 27.56% to a negative value at 27.57%, the rate of return will lie between 27.56% to 27.57%. However, since the value of -$12.52 is very close to 0, we will take the final rate of return as 27.57%

Answer is 27.57%.

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