Let's go through the problem step by step for each given scenario. Holly invested \[tex]$240,000 and Luke invested \$[/tex]80,000, and their total net income for the year is \[tex]$380,000.
### a. No agreement concerning division of net income
Without any specified agreement, the net income should be divided based on the ratio of their initial investments.
1. Calculate the total investment:
\[ \$[/tex]240,000 + \[tex]$80,000 = \$[/tex]320,000 \]
2. Calculate Holly's share:
[tex]\[ \left( \frac{\$240,000}{\$320,000} \right) \times \$380,000 = 0.75 \times \$380,000 = \$285,000 \][/tex]
3. Calculate Luke's share:
[tex]\[ \left( \frac{\$80,000}{\$320,000} \right) \times \$380,000 = 0.25 \times \$380,000 = \$95,000 \][/tex]
So, their shares are:
- Holly: \[tex]$285,000
- Luke: \$[/tex]95,000
### b. Divided in the ratio of original capital investment
This is essentially the same as the first scenario since they are being divided based on their initial investments.
So, their shares are:
- Holly: \[tex]$285,000
- Luke: \$[/tex]95,000
### c. Interest at the rate of 15% allowed on original investments and the remainder divided in the ratio of 2:3 (2/5 to Holly and 3/5 to Luke)
1. Calculate the interest for Holly:
[tex]\[ 0.15 \times \$240,000 = \$36,000 \][/tex]
2. Calculate the interest for Luke:
[tex]\[ 0.15 \times \$80,000 = \$12,000 \][/tex]
3. Subtract the total interest from the net income:
[tex]\[ \$380,000 - (\$36,000 + \$12,000) = \$380,000 - \$48,000 = \$332,000 \][/tex]
4. Divide the remainder in the ratio 2:3 (Holly:Luke):
- Holly's share of remainder:
[tex]\[ \left( \frac{2}{5} \right) \times \$332,000 = 0.4 \times \$332,000 = \$132,800 \][/tex]
- Luke's share of remainder:
[tex]\[ \left( \frac{3}{5} \right) \times \$332,000 = 0.6 \times \$332,000 = \$199,200 \][/tex]
5. Add the interest to their shares:
- Holly's total share:
[tex]\[ \$36,000 + \$132,800 = \$168,800 \][/tex]
- Luke's total share:
[tex]\[ \$12,000 + \$199,200 = \$211,200 \][/tex]
### d. Salary allowances of \[tex]$50,000 and \$[/tex]70,000, respectively, and the balance divided equally
1. Subtract the total salary allowances from the net income:
[tex]\[ \$380,000 - (\$50,000 + \$70,000) = \$380,000 - \$120,000 = \$260,000 \][/tex]
2. Divide the remaining income equally:
- Holly's share of the remainder:
[tex]\[ \frac{\$260,000}{2} = \$130,000 \][/tex]
- Luke's share of the remainder:
[tex]\[ \frac{\$260,000}{2} = \$130,000 \][/tex]
3. Add the salary allowances to their shares:
- Holly's total share:
[tex]\[ \$50,000 + \$130,000 = \$180,000 \][/tex]
- Luke's total share:
[tex]\[ \$70,000 + \$130,000 = \$200,000 \][/tex]
### e. Allowance of interest at the rate of 15% on original investments, salary allowances of \[tex]$50,000 and \$[/tex]70,000, respectively, and the remainder divided equally
1. Calculate the interest for Holly and Luke as in part c:
- Holly's interest: \[tex]$36,000
- Luke's interest: \$[/tex]12,000
2. Subtract the interest and salary allowances from the net income:
[tex]\[ \$380,000 - (\$36,000 + \$12,000 + \$50,000 + \$70,000) = \$380,000 - \$168,000 = \$212,000 \][/tex]
3. Divide the remaining income equally:
- Holly's share of the remainder:
[tex]\[ \frac{\$212,000}{2} = \$106,000 \][/tex]
- Luke’s share of the remainder:
[tex]\[ \frac{\$212,000}{2} = \$106,000 \][/tex]
4. Add the interest and salary allowances to their shares:
- Holly's total share:
[tex]\[ \$36,000 + \$50,000 + \$106,000 = \$192,000 \][/tex]
- Luke's total share:
[tex]\[ \$12,000 + \$70,000 + \$106,000 = \$188,000 \][/tex]
To summarize:
- a. No agreement:
- Holly: \[tex]$285,000
- Luke: \$[/tex]95,000
- b. Ratio of original investment:
- Holly: \[tex]$285,000
- Luke: \$[/tex]95,000
- c. Interest and remainder in 2:3 ratio:
- Holly: \[tex]$168,800
- Luke: \$[/tex]211,200
- d. Salary allowances and remainder equally:
- Holly: \[tex]$180,000
- Luke: \$[/tex]200,000
- e. Interest, salary allowances, and remainder equally:
- Holly: \[tex]$192,000
- Luke: \$[/tex]188,000
