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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)?

Solutions

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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