 # BPC| 植物大战僵尸中的投资Investment in Plants vs Zombies

###### 1310 人参与  2019年08月29日 10:20  分类 : 深国交BPC社  评论

Part 1 前言 《植物大战僵尸》这款游戏中有一个花园，玩家可以在花园里种花，等花种大之后就可以将花卖掉赚钱。笔者觉得，这样的模式和现实生活中投资模型有相似之处，便准备通过游戏，来计算出种花的利润率。（其实只是想玩游戏）

In the game "Plants vs. Zombies", there is a garden in which players can plant flowers and sell them after maturity. In the author's opinion, the method of growing flowers is similar to the realistic model of investment. This idea induces the author to investigate the profit rate of growing flowers.

1 理论知识

First of all, we need to know how to calculate profit. Profit is calculated by revenue less cost, and then, we can get the profit rate by dividing profit with the cost. Then, we should know more about the cost and revenue of investment. There are two primary sources of costs. The most obvious cost is the opportunity cost of capital used in investment projects. The opportunity cost is the cost of the next best alternative forgone, that is, instead of investing the money, investors can save it into savings accounts to earn interest given by the bank. Therefore, once the investor chooses to invest the money into such a project, they automatically give up the chance of earning interest by saving. Thus, the opportunity cost is counted AS a significant part of the cost of investment. Be    sides, because of the wear and tear during usage, there will be depreciation, which reduces the value of the capital.
Similarly, there are mainly two sources of revenue in investment, the change in price and the marginal product of capital (MPK). It is reasonable for us to understand why we take into account the change in price as a source of revenue. If you buy a house for \$400,000 and sell a house for \$500,000, ceteris parIBus, you make a \$100,000 profit by the increase of market price. However, the essential part of the investment is the marginal product of capital induced by investment. MPK is the marginal increase in the real unit of production when capital increases by 1 unit. For instance, assume that a factory now occupies ten machines and produces 100 pairs of shoes per day. If now investment occurs and the factory has a new machine. Now it has 11 machines and produces 109 pairs of shoes, so by definition, the MPK of this investment is nine pairs of shoes per day. Dividend carries out a similar function in financial investment or rent revenue for real estate investment. What is common among them is that this is the main source of income when the investing object does not have a change in price. We know that investment is the behaviour of transferring wealth from today to the future, so that the timing for buying and selling is different, as well as the time periods of dividend or MPK. Thus, we should first convert all the costs and revenues to the same time point, then can we calculate the profit using cost and benefit. To simplify, we introduce the simplest method for intertemporal discounting, the present discounted value, or pdv. By dividing the future revenue with (1+r)^(t-1), in which r is the interest rate, and t is the time period of the occurring revenue, we can convert the future value of assets into today's value. So, the present discounted value is the future value divided by (1+interest rate)^((period-1). For example, an investment occurs in two years (period 3) with \$500, so the pdv = \$500 / (1+5%)² = \$453.5.

2 实验计算

We divide the lifetime of a flower into three periods. In the first period, we buy in flower, and in the third period, the flower matures, and we sell it. Therefore, the total profit equals:

(-2570) / 1 + (-20) / (1+5%) + (3880) / (1+5%)² = \$930.22676.

The total cost equals:

(-2570) / 1 + (-150) / (1+5%) + (-150) / (1+5%)² = - \$2928.912.

The profit rate equals total profit divided by total cost.

So, the profit rate equals 31.76%. 3 研究限制

The discount value in this paper does not include a parameter β to show the time preference of consumer behaviour. The more complex version which includes this parameter should look like this, pdv = Mt /β (1+r)^(t-1). Mt represents the monetary value of revenue in t period, r represents the interest rate, and t represents the time period of revenue. Further discussion requires mathematical tools that are not in the range of this paper.

In the next article, we will introduce the pricing mechanism of investing projects: how to price a bond? We will continue to use Plants vs. Zombies as an example. There are plants that we pick up during playing games as a random reward, which do not have a price. Thus, if they can be sold in the market, how can we calculate their prices? If yes, scan the QR code to add the head of the propaganda department, Hebe, then join the WeChat group.

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