Dubois Inc. has $603,300 to invest. The company is trying to decide between two

Question

Dubois Inc. has $603,300 to invest. The company is trying to decide between two alternative uses of the funds. One alternative provides $89,910 end of year for 10 years, and the other is to receive a single lump-sum payment of the entire end of the 10 years. Which alternative should Dubois select? Assume the interest rate is constant over investment. Dubois Inc. has completed the purchase of new Dell computers. The fair value of the equipment is $806,600. The purchase agreement specifies an immediate down payment of and semiannual payments of $74,246 beginning at the end of 6 months for 5 years. the interest rate, the nearest percent, used in discounting this purchase transaction? Interest rate semiannually

Explanation / Answer

IRR of the First Project:

NPA@5%=$14,438.79

NPA@6%=-$14,493.04

Difference in NPA=$14,438.79+$14,493.04=$28,931.83

Difference in rate=5%-6%=-1%

IRR=5%-$14,438.79*(-1%)/$28,931.83=5%+0.5%=5.5%

IRR second Project:

NPA @9%=-Present value Cash outflows+Present value cash inflows=-$603,300+$1,564,803*PV factor for 10 th year @9%

=-$603,300+$1,564,803*0.4224=$57,689.70

PV factor for 10 th year @9%=1/(1+0.09)10=0.4224

NPA @11%=-Present value Cash outflows+Present value cash inflows=-$603,300+$1,564,803*PV factor for 10 th year @11%

=-$603,300+$1,564,803*0.3522=-$52,200.6

PV factor for 10 th year @11%=1/(1+0.11)10=0.3522

Difference in NPA=$57,689.70-(-$52,200.6)=$109,890.37

Difference in rate=9%-11%=-2%

IRR=9%-$57,689.70*(-2%)/$109,890.37=9%+1.05%=10.05%=10%(rounding)

so The second alternative have higher IRR so the second alternative should supposed to be accepted.

NPA of First Alternative@5% Year Cash flow Pv@5% PV 0    -6,03,300      1.0000 -6,03,300.00 1         80,000      0.9524        76,190.48 2         80,000      0.9070        72,562.36 3         80,000      0.8638        69,107.01 4         80,000      0.8227        65,816.20 5         80,000      0.7835        62,682.09 6         80,000      0.7462        59,697.23 7         80,000      0.7107        56,854.51 8         80,000      0.6768        54,147.15 9         80,000      0.6446        51,568.71 10         80,000      0.6139        49,113.06        14,438.79 NPA of First Alternative@6% Year Cash flow Pv@6% PV 0    -6,03,300      1.0000 -6,03,300.00 1         80,000      0.9434        75,471.70 2         80,000      0.8900        71,199.72 3         80,000      0.8396        67,169.54 4         80,000      0.7921        63,367.49 5         80,000      0.7473        59,780.65 6         80,000      0.7050        56,396.84 7         80,000      0.6651        53,204.57 8         80,000      0.6274        50,192.99 9         80,000      0.5919        47,351.88 10         80,000      0.5584        44,671.58      -14,493.04

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