Linda Clark received $223,000 from her mother’s estate. She placed the funds into the hands of a broker, who purchased the following securities on Linda’s behalf:a. Common stock was purchased at a cost of $99,000. The stock paid no dividends, but it was sold for $161,000 at the end of three years.b. Preferred stock was purchased at its par value of $54,000. The stock paid a 6% dividend (based on par value) each year for three years. At the end of three years, the stock was sold for $39,000.c. Bonds were purchased at a cost of $70,000. The bonds paid annual interest of $1,500. After three years, the bonds were sold for $86,000.

Respuesta :

Answer:

Explanation:

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Question:

With a discount rate of 11% solve for the net present value:

Answer:

A) NPV 18,721.81

B) NPV -17.565,93

C) NPV  -3.451,97‬

Explanation:

a) we use the lump sum present value formula and then, compare against the cost.

[tex]\frac{Maturity}{(1 + rate)^{time} } = PV[/tex]  

Maturity  $161,000.00

time  3.00

rate  0.11000

[tex]\frac{161000}{(1 + 0.11)^{3} } = PV[/tex]  

PV   117,721.8124

117,721.81 - 99,000 = 18,721.81

b) We solve forthe present value of the annuity of dividends and the lump sum of the sale price.

[tex]\frac{Maturity}{(1 + rate)^{time} } = PV[/tex]  

Maturity  $39,000.00

time  3.00

rate  0.11000

[tex]\frac{39000}{(1 + 0.11)^{3} } = PV[/tex]  

PV   28,516.4639

[tex]C \times \frac{1-(1+r)^{-time} }{rate} = PV\\[/tex]

C 3,240.00

time 3

rate 0.11

[tex]3240 \times \frac{1-(1+0.11)^{-3} }{0.11} = PV\\[/tex]

PV $7,917.6357

Net present value

28,516.43 + 7,917.64 - 54,000 = -17.565,93

C) We solve forthe present value of the annuity of dividends and the lump sum of the sale price.

[tex]C \times \frac{1-(1+r)^{-time} }{rate} = PV\\[/tex]

C 1,500.00

time 3

rate 0.11

[tex]1500 \times \frac{1-(1+0.11)^{-3} }{0.11} = PV\\[/tex]

PV $3,665.5721

[tex]\frac{Maturity}{(1 + rate)^{time} } = PV[/tex]  

Maturity  $86,000.00

time  3.00

rate  0.11000

[tex]\frac{86000}{(1 + 0.11)^{3} } = PV[/tex]  

PV   62,882.4588

62,882.46 + 3,665.57 - 70,000 = -3.451,97‬