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Homework answers / question archive / What will be the gross profit margin ratio if, total sales is N$260,000 Cost of goods sold is N$200,000 and Sales returns is N$10,000 Today is January 1
What will be the gross profit margin ratio if, total sales is N$260,000 Cost of goods sold is N$200,000 and Sales returns is N$10,000
Today is January 1. Forward prices for contracts maturing in one year and two year trade at 106 and 109 respectively. The simple interest rate per year is 5% and remains constant forever. ( Indeed the yield curve is flat at 5% simple per year). The underlying security involves no holding costs, and pays no dividends. Assume the current spot price is 100 dollars today. (a) Demonstrate a way of generating arbitrage free profits over one year. (b) Generate a way of generating arbitrage free profits over two years. (c) If we were not given the spot price at date 0, but were given the two forward prices, can a strategy be created that leads to riskless arbitrage.
Answer - Gross profit margin ratio = 0.2 or 20%
Explaination -
Gross profit margin ratio = ( sales - sales return ) - cost of goods sold / (sales - sales return )
Gross profit margin ratio = ( 260000 - 10000 ) - 200000 / ( 260000 - 10000 )
Gross profit margin ratio = 250000 - 200000 / 250000
Gross profit margin ratio = 50000 / 250000
Gross profit margin ratio = 0.2 or 20%
No arbitrage forward price for 1 year = F1 = S x (1 + r) = 100 x (1 + 5%) = 105
and No arbitrage forward price for year 2 = F2 = S x (1 + r)2 = 100 x (1 + 5%)2 = 110.25
Actual prices, Fa1 = 106 and Fa2 = 109.
Part (a)
Since Fa1 > F1, the arbitrage strategy should be:
| Action | Cash flows at | |
| t = 0 | t = 1 | |
| Borrow 100 @ 5% for 1 year | 100 | -105 |
| Buy the security | -100 | |
| Short (sell) the 1 year forward contract i.e. enter into 1 year forward contract to sell @ 106 and deliver the underlying security to close out the position on maturity | 106 | |
| Net cash flows | - | 1 |
Thus you tend to gain a riskless and riskfree profit of 1 at the end of year 1 without any initial investment. This is the arbitrage profit.
Part (b)
| Action | Cash flows at | ||
| t = 0 | t = 1 | t = 2 | |
| Borrow 100 @ 5% for 1 year | 100.00 | -105.00 | |
| Buy the security | -100.00 | ||
| Short (sell) the 1 year forward contract i.e. enter into 1 year forward contract to sell @ 106 and deliver the underlying security to close out the position on maturity | 106.00 | ||
| Short (sell) the security | 100.00 | ||
| Lend 100 @ 5% for 2 years | -100.00 | 110.25 | |
| Long (buy) the 2 years forward contract i.e. enter into 2 year forward contract to buy @ 109 and use the underlying security to close out the short position on maturity | -109.00 | ||
| Net cash flows | - | 1.00 | 1.25 |
Thus you tend to generate profit of 1 and 1.25 over two years without any initial investment. This is the arbitrage profit.
Part (c)
If Fa1 = 106; expected F2 = Fa1 x (1 + r) = 106 x (1 + 5%) = 111.30 > actual Fa2 = 109
| Action | Cash flows at | |
| t = 1 | t = 2 | |
| Short (sell) the 1 year forward contract i.e. enter into 1 year forward contract to sell @ 106 | 106.00 | |
| Long (buy) the 2 years forward contract i.e. enter into 2 year forward contract to buy @ 109 and use the underlying to close the short position | -109.00 | |
| Lend 106 @ 5% for 1 year | -106.00 | 111.30 |
| Net cash flows | - | 2.30 |
Thus you tend to gain a riskless and riskfree profit of 2.30 at the end of year 2 without any initial investment. This is the arbitrage profit.
