Yes, this only is true if pirate defaults within the first week. If pirate defaults after that, PPT will have made more money to cover their loses. In order to do a better apples to apples comparison, it's easier to use compounded interest in this scenario since then it doesn't matter when pirate defaults. 7% interest compounded for 4 weeks is about 31%.
If pirate doesn't default, pirate will payout 1.31 to PPT but PPT only pays 1.28 to bond holders, so PPT makes an addition .03 per share. That's only if no default.
Case 1 - Sell 3000 shares of PPT.A at 1.038
no default: PPT makes 3000 * (.038 + .03) = 204
default: PPT loses 960 - 114 = 846
Case 2 - Put 846 btc with pirate
no default: PPT makes 846 * .31 = 262
default: PPT loses 846
Difference is 262 - 204 = 58
So if you are do compounding interests, you only lose 58 bitcoins for this round.
I concur, albeit only if they are compounding interest, which may not be the case.
Aren't you missing something? PPT didn't choose to sell the bonds as cheap as they did - they had probably hoped they would gain more in the initial bond auction. Therefore, they won't be making much of a profit for this round. It's about as simple as an eBay seller putting $100 items up for auction at a starting price of $1.
You are entirely correct - we're just trying to figure out if this particular round of bonds was profitable.
If doing compounding interest, the break-even value is 1.0528
If doing compounding interest, the break-even value is 0.9765
As far as I know, they are not using your money for the insurance, they are using their own.
If they invest all the 3113.95 they will get 4081.75 in four weeks. That's 1.36 per bond. After buy-back, they will have made (1.36 - 1.28) * 3000 = 240 BTC.
In other words, they are risking 0.32 * 3000 = 960 BTC, and if Pirate don't default they gets 240 / 960 = 25 % profit.
Can you show the math behind that break-even value?
If they invest all 3113.95 BTC and Pirate does not default, they will make 25% profit off 960 BTC held in insurance versus 31% if they simply invested 960 BTC in Pirate in the first place.