To calculate the net asset values (NAV) for investments "a" and "b," follow these steps:
### Step 1: Understand the Formula
The formula for calculating the Net Asset Value (NAV) per share:
[tex]\[ \text{NAV} = \frac{\text{Market Value of Investments} - \text{Liabilities}}{\text{Number of Shares Outstanding}} \][/tex]
### Step 2: Input the Given Data
For investment "a":
- Market Value of Investments = [tex]$5,650,000
- Liabilities = $[/tex]820,000
- Number of Shares Outstanding = 500,000
For investment "b":
- Market Value of Investments = [tex]$13,860,000
- Liabilities = $[/tex]830,000
- Number of Shares Outstanding = 890,000
### Step 3: Calculate NAV for Investment "a"
1. Subtract the liabilities from the market value of investments:
[tex]\[ 5,650,000 - 820,000 = 4,830,000 \][/tex]
2. Divide the result by the number of shares outstanding:
[tex]\[ \frac{4,830,000}{500,000} = 9.66 \][/tex]
So, the NAV for investment "a" is [tex]$9.66 per share.
### Step 4: Calculate NAV for Investment "b"
1. Subtract the liabilities from the market value of investments:
\[ 13,860,000 - 830,000 = 13,030,000 \]
2. Divide the result by the number of shares outstanding:
\[ \frac{13,030,000}{890,000} = 14.64 \]
So, the NAV for investment "b" is $[/tex]14.64 per share.
### Summary of Results
- The net asset value (NAV) for investment "a" is [tex]$9.66 per share.
- The net asset value (NAV) for investment "b" is $[/tex]14.64 per share.
These results are rounded to the nearest cent as specified.
