Daigo Dojima recently invested $5,500 in a project that ispromising to return 2.25 percent per...

Daigo Dojima recently invested $5,500 in a project that is promising to return 2.25 percent per year. The cash flows are expected to be as follows: End of Year Cash Flow 1 $1000 2 $950 3 $875 4 ??? 5 $850 Note that the 4th year cash flow is unknown. Assuming the present value of this cash flow stream is $7,500 (that is, CF0 = -7500), what is the missing cash flow value (that is, what is the cash flow at the end of the 4th year)?

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Expert Solution

The cash flow is computed as follows:

Present value = future value / (1 + r)ⁿ

$ 7,500 = $ 1,000 / 1.0225 + $ 950 / 1.0225² + $ 875 / 1.0225³ + Year 4 cash flow / 1.0225⁴ + $ 850 / 1.0225⁵

$ 7,500 = $ 977.99511 + $ 908.6507135 + $ 818.4989055 + Year 4 cash flow x 0.914843345 + $ 760.5054704

$ 7,500 = $ 3,465.650199 + Year 4 cash flow x 0.914843345

Year 4 cash flow = ($ 7,500 - $ 3,465.650199) / 0.914843345

Year 4 cash flow = $ 4,409.88047

jeff jeffy answered 2 years ago

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