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xiaodi · 2023年08月11日

No further growth is assumed thereafter为什么仍然用terminal cap rate？

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NO.PZ201601050300000210

问题如下：

10. Based upon Exhibit 1 and Assumptions 1 and 2, the value of Property B using the discounted cash flow method, assuming a five-year holding

period, is closest to:

选项：

A.

£4,708,700.

B.

£5,035,600.

C.

£5,050,900.

解释：

B is correct.

The value of Property B using the discounted cash flow method is £5,035,600.

The value using the discounted cash flow method is based on the present value of the net operating income (NOI) and the estimated property resale price.

Calculate NOI (constant during five-year holding period from Assumption 2)

NOI = rental income (at full occupancy) + other income – vacancy and collection loss – property management fee – other operating expenses

NOI = £610,000 + £183,000 – £61,000 – £35,000 – £234,000 = £463,000

Estimate property value at end of five years:

NOI starting in year 6 is 20% higher due to lease rollovers (from Assumption 2)

NOI starting in year 6 = £463,000 × 1.20 = £555,600

Terminal cap rate (given) = 11%

Applying the terminal cap rate yields a property value of £5,050,909 (= £555,600/0.11)

Find the present value of the expected annual NOI and the estimated property resale value using the given discount rate of 9.25%:

N = 5

FV = £5,050,909

PMT = £463,000

I = 9.25

Solving for PV, the current value of the property is estimated to be £5,034,643, or £5,034,600 rounded.

考点：现金流折现法估计房地产价值

解析：可以按照以下思路进行计算，注意计算terminal value需要使用terminal cap rate, 而不是going-in cap rate.

Step 1: 计算NOI

net operating income (NOI) = rental income + other income – vacancy and collection loss – property management costs

NOI = £610,000 + £183,000 – £61,000 – £35,000 – £234,000 = £463,000

Step 2: 计算终值

第五年末的终值 terminal value = £463,000*(1+20%)/11%= £5,050,909

注意这里 1.相当于投资期结束卖给下一个投资者的价值的折现，所以这里用terminal cap rate 2 .从第六年开始，NOI增长20%。

Step 3：直接用计算器CF计算value，I/Y=9.25%, N = 5, FV = £5,050,909, PMT = £463,000, => CPT PV = £5,034,643，约算成£5,034,600.

这句话结合前面那句一次性20%增长的意思我理解的是：

第六年的NOI是第五年的1.2倍，往后每年的NOI不会有增长，所以跟第六年一样。

这样的话terminal value其实就是个永续的第六年NOI，应该用NOI6 / r 即可。

为什么要用terminal cap rate，这个cap rate隐含了一个g，但是不是没有g吗？

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Lucky_品职助教 · 2023年08月15日

嗨，从没放弃的小努力你好：


cap rate是房地产估值特有的折现率，这里的cap rate就是股票估值中的r

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努力的时光都是限量版，加油！

Lucky_品职助教 · 2023年08月11日

嗨，爱思考的PZer你好：


在使用现金流折现法估计房地产价值时，通常会使用终值（terminal value）来表示投资期结束后的持续价值。终值是通过将最后一个现金流乘以一个称为终端资本化率（terminal cap rate）的因素得出的。终端资本化率反映了预期未来收益的折现率。

在这道题中，终值的计算基于第六年开始的净经营收入（NOI）增长20%的假设（根据Assumption 2）。终值的计算公式为：终值 = 第六年的NOI / 终端资本化率。

在这里，使用终端资本化率是为了折现未来收益流，而不再考虑增长率。终端资本化率隐含了一个增长率（g），它代表了未来现金流的稳定增长率。这是因为在实际应用中，假设房地产市场的现金流会以一定速度增长，而终端资本化率则考虑了这个增长率。

因此，在计算终值时使用终端资本化率是为了符合现实情况下投资者对未来现金流的估计，确保将未来现金流以适当的折现率计算进去。

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努力的时光都是限量版，加油！

xiaodi · 2023年08月11日

我想说的就是No further growth is assumed thereafter代表了未来的NOI都是一样的，没有g 我把这当成了一个明确的考点，因为如果未来的NOU都一样，就像一个优先股一样，用NOI / r 就行了 one time increase in year 6 + No further growth is assumed thereafter，这两句话代表了我说的意思。 至于一般来说求终值要除terminal cap rate，我非常清楚。我的意思是这道题明确了“没有g”，为什么仍然用terminal cap rate

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