Answer:
Following are the solution to this question:
Explanation:
Assume that
will be a 12-month for the spot rate:
![\to 1.25 \% \times \frac{100}{2} \times 0.99 + \frac{(1.25\% \times \frac{100}{2}+100)}{(1+\frac{r_1}{2})^2}=98\\\\\to \frac{1.25}{100} \times \frac{100}{2} \times 0.99 + \frac{(\frac{1.25}{100} \times \frac{100}{2}+100)}{(1+\frac{r_1}{2})^2}=98\\\\\to \frac{1.25}{2} \times 0.99 + \frac{(\frac{1.25}{2} +100)}{(1+\frac{r_1}{2})^2}=98\\\\\to 0.61875 + \frac{( 0.625 +100)}{(\frac{2+r_1}{2})^2}=98\\\\\to 0.61875 + \frac{( 100.625)}{(\frac{2+r_1}{2})^2}=98\\\\\to 0.61875 + \frac{402.5}{(2+r_1)^2}=98\\\\](https://tex.z-dn.net/?f=%5Cto%201.25%20%5C%25%20%5Ctimes%20%5Cfrac%7B100%7D%7B2%7D%20%5Ctimes%200.99%20%2B%20%5Cfrac%7B%281.25%5C%25%20%5Ctimes%20%5Cfrac%7B100%7D%7B2%7D%2B100%29%7D%7B%281%2B%5Cfrac%7Br_1%7D%7B2%7D%29%5E2%7D%3D98%5C%5C%5C%5C%5Cto%20%5Cfrac%7B1.25%7D%7B100%7D%20%5Ctimes%20%5Cfrac%7B100%7D%7B2%7D%20%5Ctimes%200.99%20%2B%20%5Cfrac%7B%28%5Cfrac%7B1.25%7D%7B100%7D%20%5Ctimes%20%5Cfrac%7B100%7D%7B2%7D%2B100%29%7D%7B%281%2B%5Cfrac%7Br_1%7D%7B2%7D%29%5E2%7D%3D98%5C%5C%5C%5C%5Cto%20%5Cfrac%7B1.25%7D%7B2%7D%20%5Ctimes%200.99%20%2B%20%5Cfrac%7B%28%5Cfrac%7B1.25%7D%7B2%7D%20%2B100%29%7D%7B%281%2B%5Cfrac%7Br_1%7D%7B2%7D%29%5E2%7D%3D98%5C%5C%5C%5C%5Cto%200.61875%20%2B%20%5Cfrac%7B%28%200.625%20%2B100%29%7D%7B%28%5Cfrac%7B2%2Br_1%7D%7B2%7D%29%5E2%7D%3D98%5C%5C%5C%5C%5Cto%200.61875%20%2B%20%5Cfrac%7B%28%20100.625%29%7D%7B%28%5Cfrac%7B2%2Br_1%7D%7B2%7D%29%5E2%7D%3D98%5C%5C%5C%5C%5Cto%200.61875%20%2B%20%5Cfrac%7B402.5%7D%7B%282%2Br_1%29%5E2%7D%3D98%5C%5C%5C%5C)
![\to 0.61875 + \frac{402.5}{(2+r_1)^2}=98\\\\\to 0.61875 -98 = \frac{402.5}{(2+r_1)^2}\\\\\to -97.38125= \frac{402.5}{(2+r_1)^2}\\\\\to (2+r_1)^2= \frac{402.5}{ -97.38125}\\\\\to (2+r_1)^2= -4.13\\\\ \to r_1=3.304\%](https://tex.z-dn.net/?f=%5Cto%200.61875%20%2B%20%5Cfrac%7B402.5%7D%7B%282%2Br_1%29%5E2%7D%3D98%5C%5C%5C%5C%5Cto%200.61875%20-98%20%3D%20%5Cfrac%7B402.5%7D%7B%282%2Br_1%29%5E2%7D%5C%5C%5C%5C%5Cto%20-97.38125%3D%20%5Cfrac%7B402.5%7D%7B%282%2Br_1%29%5E2%7D%5C%5C%5C%5C%5Cto%20%282%2Br_1%29%5E2%3D%20%5Cfrac%7B402.5%7D%7B%20-97.38125%7D%5C%5C%5C%5C%5Cto%20%282%2Br_1%29%5E2%3D%20-4.13%5C%5C%5C%5C%20%5Cto%20r_1%3D3.304%5C%25)
Assume that
will be a 18-month for the spot rate:
![\to 1.5\% \times \frac{100}{2} \times 0.99+1.5\% \times \frac{100}{2} \times \frac{1}{(1+ \frac{3.300\%}{2})^2}+\frac{(1.5\% \times \frac{100}{2}+100)}{(1+\frac{r_2}{2})^3}=97\\\\\to \frac{1.5}{100} \times \frac{100}{2} \times 0.99+\frac{1.5}{100} \times \frac{100}{2} \times \frac{1}{(1+ \frac{\frac{3.300}{100}}{2})^2}+\frac{(\frac{1.5}{100} \times \frac{100}{2}+100)}{(1+\frac{r_2}{2})^3}=97\\\\](https://tex.z-dn.net/?f=%5Cto%201.5%5C%25%20%5Ctimes%20%5Cfrac%7B100%7D%7B2%7D%20%5Ctimes%200.99%2B1.5%5C%25%20%20%5Ctimes%20%5Cfrac%7B100%7D%7B2%7D%20%5Ctimes%20%5Cfrac%7B1%7D%7B%281%2B%20%5Cfrac%7B3.300%5C%25%7D%7B2%7D%29%5E2%7D%2B%5Cfrac%7B%281.5%5C%25%20%20%5Ctimes%20%20%5Cfrac%7B100%7D%7B2%7D%2B100%29%7D%7B%281%2B%5Cfrac%7Br_2%7D%7B2%7D%29%5E3%7D%3D97%5C%5C%5C%5C%5Cto%20%5Cfrac%7B1.5%7D%7B100%7D%20%5Ctimes%20%5Cfrac%7B100%7D%7B2%7D%20%5Ctimes%200.99%2B%5Cfrac%7B1.5%7D%7B100%7D%20%20%5Ctimes%20%5Cfrac%7B100%7D%7B2%7D%20%5Ctimes%20%5Cfrac%7B1%7D%7B%281%2B%20%5Cfrac%7B%5Cfrac%7B3.300%7D%7B100%7D%7D%7B2%7D%29%5E2%7D%2B%5Cfrac%7B%28%5Cfrac%7B1.5%7D%7B100%7D%20%20%5Ctimes%20%20%5Cfrac%7B100%7D%7B2%7D%2B100%29%7D%7B%281%2B%5Cfrac%7Br_2%7D%7B2%7D%29%5E3%7D%3D97%5C%5C%5C%5C)
![\to \frac{1.5}{2} \times 0.99+\frac{1.5}{2}\times \frac{1}{(1+ \frac{\frac{3.300}{100}}{2})^2}+\frac{(\frac{1.5}{2} +100)}{(1+\frac{r_2}{2})^3}=97\\\\\to 0.7425+0.75 \times \frac{1}{(1+ \frac{\frac{3.300}{100}}{2})^2}+\frac{(0.75 +100)}{(1+\frac{r_2}{2})^3}=97\\\\\to 1.4925 \times \frac{1}{(1+0.0165)^2}+\frac{(100.75 )}{(1+\frac{r_2}{2})^3}=97\\\\\to 1.4925 \times \frac{1}{(1.033)}+\frac{(100.75 )}{(1+\frac{r_2}{2})^3}=97\\\\](https://tex.z-dn.net/?f=%5Cto%20%5Cfrac%7B1.5%7D%7B2%7D%20%20%5Ctimes%200.99%2B%5Cfrac%7B1.5%7D%7B2%7D%5Ctimes%20%5Cfrac%7B1%7D%7B%281%2B%20%5Cfrac%7B%5Cfrac%7B3.300%7D%7B100%7D%7D%7B2%7D%29%5E2%7D%2B%5Cfrac%7B%28%5Cfrac%7B1.5%7D%7B2%7D%20%2B100%29%7D%7B%281%2B%5Cfrac%7Br_2%7D%7B2%7D%29%5E3%7D%3D97%5C%5C%5C%5C%5Cto%200.7425%2B0.75%20%5Ctimes%20%5Cfrac%7B1%7D%7B%281%2B%20%5Cfrac%7B%5Cfrac%7B3.300%7D%7B100%7D%7D%7B2%7D%29%5E2%7D%2B%5Cfrac%7B%280.75%20%20%2B100%29%7D%7B%281%2B%5Cfrac%7Br_2%7D%7B2%7D%29%5E3%7D%3D97%5C%5C%5C%5C%5Cto%201.4925%20%5Ctimes%20%5Cfrac%7B1%7D%7B%281%2B0.0165%29%5E2%7D%2B%5Cfrac%7B%28100.75%20%29%7D%7B%281%2B%5Cfrac%7Br_2%7D%7B2%7D%29%5E3%7D%3D97%5C%5C%5C%5C%5Cto%201.4925%20%5Ctimes%20%5Cfrac%7B1%7D%7B%281.033%29%7D%2B%5Cfrac%7B%28100.75%20%29%7D%7B%281%2B%5Cfrac%7Br_2%7D%7B2%7D%29%5E3%7D%3D97%5C%5C%5C%5C)
![\to 1.4925 \times 0.96+\frac{(100.75 )}{(1+\frac{r_2}{2})^3}=97\\\\\to 1.4328+\frac{(100.75 )}{(1+\frac{r_2}{2})^3}=97\\\\\to 1.4328-97= \frac{(100.75 )}{(1+\frac{r_2}{2})^3}\\\\\to -95.5672= \frac{(100.75 )}{(1+\frac{r_2}{2})^3}\\\\\to (1+\frac{r_2}{2})^3= -1.054\\\\\to r_2=3.577\%](https://tex.z-dn.net/?f=%5Cto%201.4925%20%5Ctimes%200.96%2B%5Cfrac%7B%28100.75%20%29%7D%7B%281%2B%5Cfrac%7Br_2%7D%7B2%7D%29%5E3%7D%3D97%5C%5C%5C%5C%5Cto%201.4328%2B%5Cfrac%7B%28100.75%20%29%7D%7B%281%2B%5Cfrac%7Br_2%7D%7B2%7D%29%5E3%7D%3D97%5C%5C%5C%5C%5Cto%201.4328-97%3D%20%5Cfrac%7B%28100.75%20%29%7D%7B%281%2B%5Cfrac%7Br_2%7D%7B2%7D%29%5E3%7D%5C%5C%5C%5C%5Cto%20-95.5672%3D%20%5Cfrac%7B%28100.75%20%29%7D%7B%281%2B%5Cfrac%7Br_2%7D%7B2%7D%29%5E3%7D%5C%5C%5C%5C%5Cto%20%281%2B%5Cfrac%7Br_2%7D%7B2%7D%29%5E3%3D%20-1.054%5C%5C%5C%5C%5Cto%20r_2%3D3.577%5C%25)
Assume that
will be a 18-month for the spot rate:
![\to 1.25\% \times \frac{100}{2} \times 0.99+1.25\% \times \frac{100}{2} \times \frac{1}{(1+\frac{3.300\%}{2})^2}+1.25\%\times\frac{100}{2} \times \frac{1}{(1+\frac{3.577\%}{2})^3}+(1.25\% \times \frac{\frac{100}{2}+100}{(1+\frac{r_3}{2})^4})=96\\\\](https://tex.z-dn.net/?f=%5Cto%201.25%5C%25%20%5Ctimes%20%5Cfrac%7B100%7D%7B2%7D%20%5Ctimes%200.99%2B1.25%5C%25%20%5Ctimes%20%5Cfrac%7B100%7D%7B2%7D%20%5Ctimes%20%5Cfrac%7B1%7D%7B%281%2B%5Cfrac%7B3.300%5C%25%7D%7B2%7D%29%5E2%7D%2B1.25%5C%25%5Ctimes%5Cfrac%7B100%7D%7B2%7D%20%5Ctimes%20%5Cfrac%7B1%7D%7B%281%2B%5Cfrac%7B3.577%5C%25%7D%7B2%7D%29%5E3%7D%2B%281.25%5C%25%20%5Ctimes%20%5Cfrac%7B%5Cfrac%7B100%7D%7B2%7D%2B100%7D%7B%281%2B%5Cfrac%7Br_3%7D%7B2%7D%29%5E4%7D%29%3D96%5C%5C%5C%5C)
to solve this we get ![r_3=3.335\%](https://tex.z-dn.net/?f=r_3%3D3.335%5C%25)
Out of sheer process of elimination , my best guess would be
A. machines allow the same number of workers to check more products
Answer:
total weight of debt = 0.343 or 34.3%
Explanation:
stock's market value = 17,500 x $69 = $1,207,500
bond₁'s market value = $250,000 x 101.5% = $256,750
bond₂'s market value = $350,000 x 106.5% = $372,750
total market value of the firm = $1,837,000
weighted capital structure:
market value weight
stocks $1,207,500 0.657
bond₁ $256,750 0.140
bond₂ $372,750 0.203
total $1,837,000 1
total weight of debt = 0.343 or 34.3%
C is the correct answer because it really varies depending on the game.
Privately owned businesses are commonly found in capitalist economies.